# Calculus Examples

By the Sum Rule, the derivative of with respect to is .

Evaluate .

Since is constant with respect to , the derivative of with respect to is .

Differentiate using the Power Rule which states that is where .

Multiply by .

Evaluate .

Since is constant with respect to , the derivative of with respect to is .

Differentiate using the Power Rule which states that is where .

Multiply by .

Differentiate.

Differentiate using the Power Rule which states that is where .

Since is constant with respect to , the derivative of with respect to is .

Simplify.

Add and .

Reorder terms.

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

Split into separate intervals around the values that make the first derivative or undefined.

Replace the variable with in the expression.

Simplify the result.

Simplify each term.

Raising to any positive power yields .

Multiply by .

Raising to any positive power yields .

Multiply by .

Simplify by adding numbers.

Add and .

Add and .

The final answer is .

Replace the variable with in the expression.

Simplify the result.

Simplify each term.

Raise to the power of .

Multiply by .

Raise to the power of .

Multiply by .

Simplify by adding numbers.

Add and .

Add and .

The final answer is .

Since the first derivative changed signs from positive to negative around , then there is a turning point at .

Find to find the y-coordinate of .

Replace the variable with in the expression.

Simplify .

Remove parentheses.

Simplify each term.

Raise to the power of .

Multiply by .

Raise to the power of .

Multiply by .

Simplify by adding and subtracting.

Subtract from .

Add and .

Add and .

Write the and coordinates in point form.