Calculus Examples

$y = \frac{4 {(x)}^{3}}{{(x - 1)}^{2}}$

Step 1

Remove parentheses.

$y = \frac{4 x^{3}}{{(x - 1)}^{2}}$

Step 2

Differentiate both sides of the equation.

$\frac{d}{d x} (y) = \frac{d}{d x} (\frac{4 x^{3}}{{(x - 1)}^{2}})$

Step 3

The derivative of $y$ with respect to $x$ is $y'$ .

$y'$

Step 4

Differentiate the right side of the equation.

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Step 4.1

Since $4$ is constant with respect to $x$ , the derivative of $\frac{4 x^{3}}{{(x - 1)}^{2}}$ with respect to $x$ is $4 \frac{d}{d x} [\frac{x^{3}}{{(x - 1)}^{2}}]$ .

$4 \frac{d}{d x} [\frac{x^{3}}{{(x - 1)}^{2}}]$

Step 4.2

Differentiate using the Quotient Rule which states that $\frac{d}{d x} [\frac{f (x)}{g (x)}]$ is $\frac{g (x) \frac{d}{d x} [f (x)] - f (x) \frac{d}{d x} [g (x)]}{{g (x)}^{2}}$ where $f (x) = x^{3}$ and $g (x) = {(x - 1)}^{2}$ .

$4 \frac{{(x - 1)}^{2} \frac{d}{d x} [x^{3}] - x^{3} \frac{d}{d x} [{(x - 1)}^{2}]}{{({(x - 1)}^{2})}^{2}}$

Step 4.3

Differentiate using the Power Rule.

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Step 4.3.1

Multiply the exponents in ${({(x - 1)}^{2})}^{2}$ .

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Step 4.3.1.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$4 \frac{{(x - 1)}^{2} \frac{d}{d x} [x^{3}] - x^{3} \frac{d}{d x} [{(x - 1)}^{2}]}{{(x - 1)}^{2 \cdot 2}}$

Step 4.3.1.2

Multiply $2$ by $2$ .

$4 \frac{{(x - 1)}^{2} \frac{d}{d x} [x^{3}] - x^{3} \frac{d}{d x} [{(x - 1)}^{2}]}{{(x - 1)}^{4}}$

Step 4.3.2

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 3$ .

$4 \frac{{(x - 1)}^{2} (3 x^{2}) - x^{3} \frac{d}{d x} [{(x - 1)}^{2}]}{{(x - 1)}^{4}}$

Step 4.3.3

Move $3$ to the left of ${(x - 1)}^{2}$ .

$4 \frac{3 \cdot {(x - 1)}^{2} x^{2} - x^{3} \frac{d}{d x} [{(x - 1)}^{2}]}{{(x - 1)}^{4}}$

Step 4.4

Differentiate using the chain rule, which states that $\frac{d}{d x} [f (g (x))]$ is $f' (g (x)) g' (x)$ where $f (x) = x^{2}$ and $g (x) = x - 1$ .

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Step 4.4.1

To apply the Chain Rule, set $u$ as $x - 1$ .

$4 \frac{3 {(x - 1)}^{2} x^{2} - x^{3} (\frac{d}{d u} [u^{2}] \frac{d}{d x} [x - 1])}{{(x - 1)}^{4}}$

Step 4.4.2

Differentiate using the Power Rule which states that $\frac{d}{d u} [u^{n}]$ is $n u^{n - 1}$ where $n = 2$ .

$4 \frac{3 {(x - 1)}^{2} x^{2} - x^{3} (2 u \frac{d}{d x} [x - 1])}{{(x - 1)}^{4}}$

Step 4.4.3

Replace all occurrences of $u$ with $x - 1$ .

$4 \frac{3 {(x - 1)}^{2} x^{2} - x^{3} (2 (x - 1) \frac{d}{d x} [x - 1])}{{(x - 1)}^{4}}$

Step 4.5

Differentiate.

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Step 4.5.1

Multiply $2$ by $- 1$ .

$4 \frac{3 {(x - 1)}^{2} x^{2} - 2 x^{3} ((x - 1) \frac{d}{d x} [x - 1])}{{(x - 1)}^{4}}$

Step 4.5.2

By the Sum Rule, the derivative of $x - 1$ with respect to $x$ is $\frac{d}{d x} [x] + \frac{d}{d x} [- 1]$ .

$4 \frac{3 {(x - 1)}^{2} x^{2} - 2 x^{3} ((x - 1) (\frac{d}{d x} [x] + \frac{d}{d x} [- 1]))}{{(x - 1)}^{4}}$

Step 4.5.3

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 1$ .

$4 \frac{3 {(x - 1)}^{2} x^{2} - 2 x^{3} ((x - 1) (1 + \frac{d}{d x} [- 1]))}{{(x - 1)}^{4}}$

Step 4.5.4

Since $- 1$ is constant with respect to $x$ , the derivative of $- 1$ with respect to $x$ is $0$ .

$4 \frac{3 {(x - 1)}^{2} x^{2} - 2 x^{3} ((x - 1) (1 + 0))}{{(x - 1)}^{4}}$

Step 4.5.5

Combine fractions.

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Step 4.5.5.1

Add $1$ and $0$ .

$4 \frac{3 {(x - 1)}^{2} x^{2} - 2 x^{3} ((x - 1) \cdot 1)}{{(x - 1)}^{4}}$

Step 4.5.5.2

Multiply $x - 1$ by $1$ .

$4 \frac{3 {(x - 1)}^{2} x^{2} - 2 x^{3} (x - 1)}{{(x - 1)}^{4}}$

Step 4.5.5.3

Combine $4$ and $\frac{3 {(x - 1)}^{2} x^{2} - 2 x^{3} (x - 1)}{{(x - 1)}^{4}}$ .

$\frac{4 (3 {(x - 1)}^{2} x^{2} - 2 x^{3} (x - 1))}{{(x - 1)}^{4}}$

Step 4.6

Simplify.

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Step 4.6.1

Apply the distributive property.

$\frac{4 (3 {(x - 1)}^{2} x^{2} - 2 x^{3} x - 2 x^{3} \cdot - 1)}{{(x - 1)}^{4}}$

Step 4.6.2

Apply the distributive property.

$\frac{4 (3 {(x - 1)}^{2} x^{2}) + 4 (- 2 x^{3} x) + 4 (- 2 x^{3} \cdot - 1)}{{(x - 1)}^{4}}$

Step 4.6.3

Simplify the numerator.

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Step 4.6.3.1

Simplify each term.

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Step 4.6.3.1.1

Rewrite ${(x - 1)}^{2}$ as $(x - 1) (x - 1)$ .

$\frac{4 (3 ((x - 1) (x - 1)) x^{2}) + 4 (- 2 x^{3} x) + 4 (- 2 x^{3} \cdot - 1)}{{(x - 1)}^{4}}$

Step 4.6.3.1.2

Expand $(x - 1) (x - 1)$ using the FOIL Method.

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Step 4.6.3.1.2.1

Apply the distributive property.

$\frac{4 (3 (x (x - 1) - 1 (x - 1)) x^{2}) + 4 (- 2 x^{3} x) + 4 (- 2 x^{3} \cdot - 1)}{{(x - 1)}^{4}}$

Step 4.6.3.1.2.2

Apply the distributive property.

$\frac{4 (3 (x \cdot x + x \cdot - 1 - 1 (x - 1)) x^{2}) + 4 (- 2 x^{3} x) + 4 (- 2 x^{3} \cdot - 1)}{{(x - 1)}^{4}}$

Step 4.6.3.1.2.3

Apply the distributive property.

$\frac{4 (3 (x \cdot x + x \cdot - 1 - 1 x - 1 \cdot - 1) x^{2}) + 4 (- 2 x^{3} x) + 4 (- 2 x^{3} \cdot - 1)}{{(x - 1)}^{4}}$

Step 4.6.3.1.3

Simplify and combine like terms.

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Step 4.6.3.1.3.1

Simplify each term.

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Step 4.6.3.1.3.1.1

Multiply $x$ by $x$ .

$\frac{4 (3 (x^{2} + x \cdot - 1 - 1 x - 1 \cdot - 1) x^{2}) + 4 (- 2 x^{3} x) + 4 (- 2 x^{3} \cdot - 1)}{{(x - 1)}^{4}}$

Step 4.6.3.1.3.1.2

Move $- 1$ to the left of $x$ .

$\frac{4 (3 (x^{2} - 1 \cdot x - 1 x - 1 \cdot - 1) x^{2}) + 4 (- 2 x^{3} x) + 4 (- 2 x^{3} \cdot - 1)}{{(x - 1)}^{4}}$

Step 4.6.3.1.3.1.3

Rewrite $- 1 x$ as $- x$ .

$\frac{4 (3 (x^{2} - x - 1 x - 1 \cdot - 1) x^{2}) + 4 (- 2 x^{3} x) + 4 (- 2 x^{3} \cdot - 1)}{{(x - 1)}^{4}}$

Step 4.6.3.1.3.1.4

Rewrite $- 1 x$ as $- x$ .

$\frac{4 (3 (x^{2} - x - x - 1 \cdot - 1) x^{2}) + 4 (- 2 x^{3} x) + 4 (- 2 x^{3} \cdot - 1)}{{(x - 1)}^{4}}$

Step 4.6.3.1.3.1.5

Multiply $- 1$ by $- 1$ .

$\frac{4 (3 (x^{2} - x - x + 1) x^{2}) + 4 (- 2 x^{3} x) + 4 (- 2 x^{3} \cdot - 1)}{{(x - 1)}^{4}}$

Step 4.6.3.1.3.2

Subtract $x$ from $- x$ .

$\frac{4 (3 (x^{2} - 2 x + 1) x^{2}) + 4 (- 2 x^{3} x) + 4 (- 2 x^{3} \cdot - 1)}{{(x - 1)}^{4}}$

Step 4.6.3.1.4

Apply the distributive property.

$\frac{4 ((3 x^{2} + 3 (- 2 x) + 3 \cdot 1) x^{2}) + 4 (- 2 x^{3} x) + 4 (- 2 x^{3} \cdot - 1)}{{(x - 1)}^{4}}$

Step 4.6.3.1.5

Simplify.

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Step 4.6.3.1.5.1

Multiply $- 2$ by $3$ .

$\frac{4 ((3 x^{2} - 6 x + 3 \cdot 1) x^{2}) + 4 (- 2 x^{3} x) + 4 (- 2 x^{3} \cdot - 1)}{{(x - 1)}^{4}}$

Step 4.6.3.1.5.2

Multiply $3$ by $1$ .

$\frac{4 ((3 x^{2} - 6 x + 3) x^{2}) + 4 (- 2 x^{3} x) + 4 (- 2 x^{3} \cdot - 1)}{{(x - 1)}^{4}}$

Step 4.6.3.1.6

Apply the distributive property.

$\frac{4 (3 x^{2} x^{2} - 6 x \cdot x^{2} + 3 x^{2}) + 4 (- 2 x^{3} x) + 4 (- 2 x^{3} \cdot - 1)}{{(x - 1)}^{4}}$

Step 4.6.3.1.7

Simplify.

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Step 4.6.3.1.7.1

Multiply $x^{2}$ by $x^{2}$ by adding the exponents.

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Step 4.6.3.1.7.1.1

Move $x^{2}$ .

$\frac{4 (3 (x^{2} x^{2}) - 6 x \cdot x^{2} + 3 x^{2}) + 4 (- 2 x^{3} x) + 4 (- 2 x^{3} \cdot - 1)}{{(x - 1)}^{4}}$

Step 4.6.3.1.7.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{4 (3 x^{2 + 2} - 6 x \cdot x^{2} + 3 x^{2}) + 4 (- 2 x^{3} x) + 4 (- 2 x^{3} \cdot - 1)}{{(x - 1)}^{4}}$

Step 4.6.3.1.7.1.3

Add $2$ and $2$ .

$\frac{4 (3 x^{4} - 6 x \cdot x^{2} + 3 x^{2}) + 4 (- 2 x^{3} x) + 4 (- 2 x^{3} \cdot - 1)}{{(x - 1)}^{4}}$

Step 4.6.3.1.7.2

Multiply $x$ by $x^{2}$ by adding the exponents.

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Step 4.6.3.1.7.2.1

Move $x^{2}$ .

$\frac{4 (3 x^{4} - 6 (x^{2} x) + 3 x^{2}) + 4 (- 2 x^{3} x) + 4 (- 2 x^{3} \cdot - 1)}{{(x - 1)}^{4}}$

Step 4.6.3.1.7.2.2

Multiply $x^{2}$ by $x$ .

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Step 4.6.3.1.7.2.2.1

Raise $x$ to the power of $1$ .

$\frac{4 (3 x^{4} - 6 (x^{2} x^{1}) + 3 x^{2}) + 4 (- 2 x^{3} x) + 4 (- 2 x^{3} \cdot - 1)}{{(x - 1)}^{4}}$

Step 4.6.3.1.7.2.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{4 (3 x^{4} - 6 x^{2 + 1} + 3 x^{2}) + 4 (- 2 x^{3} x) + 4 (- 2 x^{3} \cdot - 1)}{{(x - 1)}^{4}}$

Step 4.6.3.1.7.2.3

Add $2$ and $1$ .

$\frac{4 (3 x^{4} - 6 x^{3} + 3 x^{2}) + 4 (- 2 x^{3} x) + 4 (- 2 x^{3} \cdot - 1)}{{(x - 1)}^{4}}$

Step 4.6.3.1.8

Apply the distributive property.

$\frac{4 (3 x^{4}) + 4 (- 6 x^{3}) + 4 (3 x^{2}) + 4 (- 2 x^{3} x) + 4 (- 2 x^{3} \cdot - 1)}{{(x - 1)}^{4}}$

Step 4.6.3.1.9

Simplify.

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Step 4.6.3.1.9.1

Multiply $3$ by $4$ .

$\frac{12 x^{4} + 4 (- 6 x^{3}) + 4 (3 x^{2}) + 4 (- 2 x^{3} x) + 4 (- 2 x^{3} \cdot - 1)}{{(x - 1)}^{4}}$

Step 4.6.3.1.9.2

Multiply $- 6$ by $4$ .

$\frac{12 x^{4} - 24 x^{3} + 4 (3 x^{2}) + 4 (- 2 x^{3} x) + 4 (- 2 x^{3} \cdot - 1)}{{(x - 1)}^{4}}$

Step 4.6.3.1.9.3

Multiply $3$ by $4$ .

$\frac{12 x^{4} - 24 x^{3} + 12 x^{2} + 4 (- 2 x^{3} x) + 4 (- 2 x^{3} \cdot - 1)}{{(x - 1)}^{4}}$

Step 4.6.3.1.10

Multiply $x^{3}$ by $x$ by adding the exponents.

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Step 4.6.3.1.10.1

Move $x$ .

$\frac{12 x^{4} - 24 x^{3} + 12 x^{2} + 4 (- 2 (x \cdot x^{3})) + 4 (- 2 x^{3} \cdot - 1)}{{(x - 1)}^{4}}$

Step 4.6.3.1.10.2

Multiply $x$ by $x^{3}$ .

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Step 4.6.3.1.10.2.1

Raise $x$ to the power of $1$ .

$\frac{12 x^{4} - 24 x^{3} + 12 x^{2} + 4 (- 2 (x^{1} x^{3})) + 4 (- 2 x^{3} \cdot - 1)}{{(x - 1)}^{4}}$

Step 4.6.3.1.10.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{12 x^{4} - 24 x^{3} + 12 x^{2} + 4 (- 2 x^{1 + 3}) + 4 (- 2 x^{3} \cdot - 1)}{{(x - 1)}^{4}}$

Step 4.6.3.1.10.3

Add $1$ and $3$ .

$\frac{12 x^{4} - 24 x^{3} + 12 x^{2} + 4 (- 2 x^{4}) + 4 (- 2 x^{3} \cdot - 1)}{{(x - 1)}^{4}}$

Step 4.6.3.1.11

Multiply $- 2$ by $4$ .

$\frac{12 x^{4} - 24 x^{3} + 12 x^{2} - 8 x^{4} + 4 (- 2 x^{3} \cdot - 1)}{{(x - 1)}^{4}}$

Step 4.6.3.1.12

Multiply $- 1$ by $- 2$ .

$\frac{12 x^{4} - 24 x^{3} + 12 x^{2} - 8 x^{4} + 4 (2 x^{3})}{{(x - 1)}^{4}}$

Step 4.6.3.1.13

Multiply $2$ by $4$ .

$\frac{12 x^{4} - 24 x^{3} + 12 x^{2} - 8 x^{4} + 8 x^{3}}{{(x - 1)}^{4}}$

Step 4.6.3.2

Subtract $8 x^{4}$ from $12 x^{4}$ .

$\frac{4 x^{4} - 24 x^{3} + 12 x^{2} + 8 x^{3}}{{(x - 1)}^{4}}$

Step 4.6.3.3

Add $- 24 x^{3}$ and $8 x^{3}$ .

$\frac{4 x^{4} - 16 x^{3} + 12 x^{2}}{{(x - 1)}^{4}}$

Step 4.6.4

Simplify the numerator.

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Step 4.6.4.1

Factor $4 x^{2}$ out of $4 x^{4} - 16 x^{3} + 12 x^{2}$ .

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Step 4.6.4.1.1

Factor $4 x^{2}$ out of $4 x^{4}$ .

$\frac{4 x^{2} (x^{2}) - 16 x^{3} + 12 x^{2}}{{(x - 1)}^{4}}$

Step 4.6.4.1.2

Factor $4 x^{2}$ out of $- 16 x^{3}$ .

$\frac{4 x^{2} (x^{2}) + 4 x^{2} (- 4 x) + 12 x^{2}}{{(x - 1)}^{4}}$

Step 4.6.4.1.3

Factor $4 x^{2}$ out of $12 x^{2}$ .

$\frac{4 x^{2} (x^{2}) + 4 x^{2} (- 4 x) + 4 x^{2} (3)}{{(x - 1)}^{4}}$

Step 4.6.4.1.4

Factor $4 x^{2}$ out of $4 x^{2} (x^{2}) + 4 x^{2} (- 4 x)$ .

$\frac{4 x^{2} (x^{2} - 4 x) + 4 x^{2} (3)}{{(x - 1)}^{4}}$

Step 4.6.4.1.5

Factor $4 x^{2}$ out of $4 x^{2} (x^{2} - 4 x) + 4 x^{2} (3)$ .

$\frac{4 x^{2} (x^{2} - 4 x + 3)}{{(x - 1)}^{4}}$

Step 4.6.4.2

Factor $x^{2} - 4 x + 3$ using the AC method.

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Step 4.6.4.2.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $3$ and whose sum is $- 4$ .

$- 3, - 1$

Step 4.6.4.2.2

Write the factored form using these integers.

$\frac{4 x^{2} ((x - 3) (x - 1))}{{(x - 1)}^{4}}$

$\frac{4 x^{2} (x - 3) (x - 1)}{{(x - 1)}^{4}}$

Step 4.6.5

Cancel the common factor of $x - 1$ and ${(x - 1)}^{4}$ .

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Step 4.6.5.1

Factor $x - 1$ out of $4 x^{2} (x - 3) (x - 1)$ .

$\frac{(x - 1) (4 x^{2} (x - 3))}{{(x - 1)}^{4}}$

Step 4.6.5.2

Cancel the common factors.

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Step 4.6.5.2.1

Factor $x - 1$ out of ${(x - 1)}^{4}$ .

$\frac{(x - 1) (4 x^{2} (x - 3))}{(x - 1) {(x - 1)}^{3}}$

Step 4.6.5.2.2

Cancel the common factor.

$\frac{(x - 1) (4 x^{2} (x - 3))}{(x - 1) {(x - 1)}^{3}}$

Step 4.6.5.2.3

Rewrite the expression.

$\frac{4 x^{2} (x - 3)}{{(x - 1)}^{3}}$

Step 5

Reform the equation by setting the left side equal to the right side.

$y' = \frac{4 x^{2} (x - 3)}{{(x - 1)}^{3}}$

Step 6

Replace $y'$ with $\frac{d y}{d x}$ .

$\frac{d y}{d x} = \frac{4 x^{2} (x - 3)}{{(x - 1)}^{3}}$

Step 7

Set $\frac{d y}{d x} = 0$ then solve for $x$ in terms of $y$ .

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Step 7.1

Set the numerator equal to zero.

$4 x^{2} (x - 3) = 0$

Step 7.2

Solve the equation for $x$ .

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Step 7.2.1

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x^{2} = 0$

$x - 3 = 0$

Step 7.2.2

Set $x^{2}$ equal to $0$ and solve for $x$ .

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Step 7.2.2.1

Set $x^{2}$ equal to $0$ .

$x^{2} = 0$

Step 7.2.2.2

Solve $x^{2} = 0$ for $x$ .

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Step 7.2.2.2.1

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{0}$

Step 7.2.2.2.2

Simplify $\pm \sqrt{0}$ .

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Step 7.2.2.2.2.1

Rewrite $0$ as $0^{2}$ .

$x = \pm \sqrt{0^{2}}$

Step 7.2.2.2.2.2

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm 0$

Step 7.2.2.2.2.3

Plus or minus $0$ is $0$ .

$x = 0$

Step 7.2.3

Set $x - 3$ equal to $0$ and solve for $x$ .

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Step 7.2.3.1

Set $x - 3$ equal to $0$ .

$x - 3 = 0$

Step 7.2.3.2

Add $3$ to both sides of the equation.

$x = 3$

Step 7.2.4

The final solution is all the values that make $4 x^{2} (x - 3) = 0$ true.

$x = 0, 3$

Step 8

Solve for $y$ .

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Step 8.1

Remove parentheses.

$y = \frac{4 \cdot 0^{3}}{{((0) - 1)}^{2}}$

Step 8.2

Remove parentheses.

$y = \frac{4 \cdot 0^{3}}{{(0 - 1)}^{2}}$

Step 8.3

Remove parentheses.

$y = \frac{4 {(0)}^{3}}{{((0) - 1)}^{2}}$

Step 8.4

Simplify $\frac{4 {(0)}^{3}}{{((0) - 1)}^{2}}$ .

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Step 8.4.1

Raising $0$ to any positive power yields $0$ .

$y = \frac{4 \cdot 0}{{(0 - 1)}^{2}}$

Step 8.4.2

Simplify the denominator.

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Step 8.4.2.1

Subtract $1$ from $0$ .

$y = \frac{4 \cdot 0}{{(- 1)}^{2}}$

Step 8.4.2.2

Raise $- 1$ to the power of $2$ .

$y = \frac{4 \cdot 0}{1}$

Step 8.4.3

Simplify the expression.

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Step 8.4.3.1

Multiply $4$ by $0$ .

$y = \frac{0}{1}$

Step 8.4.3.2

Divide $0$ by $1$ .

$y = 0$

Step 9

Solve for $y$ .

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Step 9.1

Remove parentheses.

$y = \frac{4 \cdot 3^{3}}{{((3) - 1)}^{2}}$

Step 9.2

Remove parentheses.

$y = \frac{4 \cdot 3^{3}}{{(3 - 1)}^{2}}$

Step 9.3

Remove parentheses.

$y = \frac{4 {(3)}^{3}}{{((3) - 1)}^{2}}$

Step 9.4

Simplify $\frac{4 {(3)}^{3}}{{((3) - 1)}^{2}}$ .

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Step 9.4.1

Raise $3$ to the power of $3$ .

$y = \frac{4 \cdot 27}{{(3 - 1)}^{2}}$

Step 9.4.2

Simplify the denominator.

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Step 9.4.2.1

Subtract $1$ from $3$ .

$y = \frac{4 \cdot 27}{2^{2}}$

Step 9.4.2.2

Raise $2$ to the power of $2$ .

$y = \frac{4 \cdot 27}{4}$

Step 9.4.3

Simplify the expression.

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Step 9.4.3.1

Multiply $4$ by $27$ .

$y = \frac{108}{4}$

Step 9.4.3.2

Divide $108$ by $4$ .

$y = 27$

Step 10

Find the points where $\frac{d y}{d x} = 0$ .

$(0, 0)$

$(3, 27)$

Step 11