# Calculus Examples

Consider the difference quotient formula. Use this formula to solve for the slope of the secant line .

Evaluate the function at .

Replace the variable with in the expression.

Simplify the result.

Simplify each term.

Rewrite as .

Expand using the FOIL Method.

Apply the distributive property.

Apply the distributive property.

Apply the distributive property.

Remove parentheses.

Simplify and combine like terms.

Simplify each term.

Multiply by by adding the exponents.

Combine and

Raise to the power of .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Multiply by by adding the exponents.

Combine and

Raise to the power of .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Add and .

Reorder and .

Add and .

The final answer is .

Find the components of the definition.

Plug in the components.

Simplify the numerator.

Apply the distributive property.

Multiply by .

Remove unnecessary parentheses.

Subtract from .

Add and .

Subtract from .

Add and .

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Reduce the expression by cancelling the common factors.

Cancel the common factor.

Divide by .