Calculus Examples

$y = x {(x - 1)}^{2}$

Step 1

Find the point at $x = - 1$ .

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Step 1.1

Replace the variable $x$ with $- 1$ in the expression.

$f (- 1) = (- 1) {((- 1) - 1)}^{2}$

Step 1.2

Simplify the result.

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Step 1.2.1

Subtract $1$ from $- 1$ .

$f (- 1) = - 1 {(- 2)}^{2}$

Step 1.2.2

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

$f (- 1) = - 1 \cdot 4$

Step 1.2.3

Multiply $- 1$ by $4$ .

$f (- 1) = - 4$

Step 1.2.4

The final answer is $- 4$ .

$- 4$

Step 1.3

Convert $- 4$ to decimal.

$y = - 4$

Step 2

Find the point at $x = 0$ .

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Step 2.1

Replace the variable $x$ with $0$ in the expression.

$f (0) = (0) {((0) - 1)}^{2}$

Step 2.2

Simplify the result.

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Step 2.2.1

Subtract $1$ from $0$ .

$f (0) = 0 {(- 1)}^{2}$

Step 2.2.2

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

$f (0) = 0 \cdot 1$

Step 2.2.3

Multiply $0$ by $1$ .

$f (0) = 0$

Step 2.2.4

The final answer is $0$ .

$0$

Step 2.3

Convert $0$ to decimal.

$y = 0$

Step 3

Find the point at $x = 2$ .

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Step 3.1

Replace the variable $x$ with $2$ in the expression.

$f (2) = (2) {((2) - 1)}^{2}$

Step 3.2

Simplify the result.

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Step 3.2.1

Subtract $1$ from $2$ .

$f (2) = 2 \cdot 1^{2}$

Step 3.2.2

One to any power is one.

$f (2) = 2 \cdot 1$

Step 3.2.3

Multiply $2$ by $1$ .

$f (2) = 2$

Step 3.2.4

The final answer is $2$ .

$2$

Step 3.3

Convert $2$ to decimal.

$y = 2$

Step 4

Find the point at $x = 3$ .

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Step 4.1

Replace the variable $x$ with $3$ in the expression.

$f (3) = (3) {((3) - 1)}^{2}$

Step 4.2

Simplify the result.

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Step 4.2.1

Subtract $1$ from $3$ .

$f (3) = 3 \cdot 2^{2}$

Step 4.2.2

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

$f (3) = 3 \cdot 4$

Step 4.2.3

Multiply $3$ by $4$ .

$f (3) = 12$

Step 4.2.4

The final answer is $12$ .

$12$

Step 4.3

Convert $12$ to decimal.

$y = 12$

Step 5

The cubic function can be graphed using the function behavior and the points.

$\begin{array}{c} x & y \\ - 1 & - 4 \\ 0 & 0 \\ 1 & 0 \\ 2 & 2 \\ 3 & 12 \end{array}$

Step 6

The cubic function can be graphed using the function behavior and the selected points.

Falls to the left and rises to the right

$\begin{array}{c} x & y \\ - 1 & - 4 \\ 0 & 0 \\ 1 & 0 \\ 2 & 2 \\ 3 & 12 \end{array}$

Step 7