Calculus Examples

$y = {(x - 6)}^{3}$

Step 1

Simplify ${(x - 6)}^{3}$ .

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Step 1.1

Use the Binomial Theorem.

$y = x^{3} + 3 x^{2} \cdot - 6 + 3 x {(- 6)}^{2} + {(- 6)}^{3}$

Step 1.2

Simplify each term.

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Step 1.2.1

Multiply $- 6$ by $3$ .

$y = x^{3} - 18 x^{2} + 3 x {(- 6)}^{2} + {(- 6)}^{3}$

Step 1.2.2

Raise $- 6$ to the power of $2$ .

$y = x^{3} - 18 x^{2} + 3 x \cdot 36 + {(- 6)}^{3}$

Step 1.2.3

Multiply $36$ by $3$ .

$y = x^{3} - 18 x^{2} + 108 x + {(- 6)}^{3}$

Step 1.2.4

Raise $- 6$ to the power of $3$ .

$y = x^{3} - 18 x^{2} + 108 x - 216$

Step 2

Graph the equation in order to determine the intervals over which it is increasing or decreasing.

Increasing on: $(- \infty, 6), (6, \infty)$

Step 3