Calculus Examples

$x^{4} - 4 x^{3} + 10$

Step 1

Write $x^{4} - 4 x^{3} + 10$ as an equation.

$y = x^{4} - 4 x^{3} + 10$

Step 2

Find the x-intercepts.

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Step 2.1

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$0 = x^{4} - 4 x^{3} + 10$

Step 2.2

Solve the equation.

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Step 2.2.1

Remove parentheses.

$0 = x^{4} - 4 x^{3} + 10$

Step 2.2.2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x \approx 1.61179337, 3.82070437$

Step 2.3

x-intercept(s) in point form.

x-intercept(s): $(1.61179337, 0), (3.82070437, 0)$

Step 3

Find the y-intercepts.

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Step 3.1

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$y = {(0)}^{4} - 4 {(0)}^{3} + 10$

Step 3.2

Solve the equation.

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Step 3.2.1

Remove parentheses.

$y = 0^{4} - 4 {(0)}^{3} + 10$

Step 3.2.2

Remove parentheses.

$y = 0^{4} - 4 \cdot 0^{3} + 10$

Step 3.2.3

Remove parentheses.

$y = {(0)}^{4} - 4 {(0)}^{3} + 10$

Step 3.2.4

Simplify ${(0)}^{4} - 4 {(0)}^{3} + 10$ .

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Step 3.2.4.1

Simplify each term.

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Step 3.2.4.1.1

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

$y = 0 - 4 {(0)}^{3} + 10$

Step 3.2.4.1.2

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

$y = 0 - 4 \cdot 0 + 10$

Step 3.2.4.1.3

Multiply $- 4$ by $0$ .

$y = 0 + 0 + 10$

Step 3.2.4.2

Simplify by adding numbers.

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Step 3.2.4.2.1

Add $0$ and $0$ .

$y = 0 + 10$

Step 3.2.4.2.2

Add $0$ and $10$ .

$y = 10$

Step 3.3

y-intercept(s) in point form.

y-intercept(s): $(0, 10)$

Step 4

List the intersections.

x-intercept(s): $(1.61179337, 0), (3.82070437, 0)$

y-intercept(s): $(0, 10)$

Step 5