# 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.

Rewrite as .

Expand using the FOIL Method.

Apply the distributive property.

Apply the distributive property.

Apply the distributive property.

Simplify and combine like terms.

Simplify each term.

Multiply by .

Multiply by .

Add and .

Reorder and .

Add and .

Apply the distributive property.

Multiply by .

The final answer is .

Find the components of the definition.

Plug in the components.

Simplify the numerator.

Group the last three terms.

Multiply by .

Subtract from .

Add and .

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Simplify terms.

Reduce the expression by cancelling the common factors.

Cancel the common factor.

Divide by .

Apply the distributive property.

Multiply by .