Calculus Examples

$y = - x^{3} + x - 5$

Step 1

Find the x-intercepts.

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Step 1.1

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

$0 = - x^{3} + x - 5$

Step 1.2

Solve the equation.

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Step 1.2.1

Remove parentheses.

$0 = - x^{3} + x - 5$

Step 1.2.2

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

$x \approx - 1.90416085$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(- 1.90416085, 0)$

Step 2

Find the y-intercepts.

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Step 2.1

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

$y = - {(0)}^{3} + 0 - 5$

Step 2.2

Solve the equation.

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Step 2.2.1

Remove parentheses.

$y = - {(0)}^{3} + 0 - 5$

Step 2.2.2

Remove parentheses.

$y = - 0^{3} + 0 - 5$

Step 2.2.3

Remove parentheses.

$y = - {(0)}^{3} + 0 - 5$

Step 2.2.4

Simplify $- {(0)}^{3} + 0 - 5$ .

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Step 2.2.4.1

Simplify each term.

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Step 2.2.4.1.1

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

$y = - 0 + 0 - 5$

Step 2.2.4.1.2

Multiply $- 1$ by $0$ .

$y = 0 + 0 - 5$

Step 2.2.4.2

Simplify by adding and subtracting.

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Step 2.2.4.2.1

Add $0$ and $0$ .

$y = 0 - 5$

Step 2.2.4.2.2

Subtract $5$ from $0$ .

$y = - 5$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, - 5)$

Step 3

List the intersections.

x-intercept(s): $(- 1.90416085, 0)$

y-intercept(s): $(0, - 5)$

Step 4