# 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.

Use the power rule to combine exponents.

Add and to get .

Use the power rule to combine exponents.

Add and to get .

Add and to get .

Reorder and .

Add and to get .

The final answer is .

Find the components of the definition.

Plug in the components.

Simplify the numerator.

Apply the distributive property.

Multiply by to get .

Remove parentheses.

Subtract from to get .

Add and to get .

Subtract from to get .

Add and to get .

Factor out of .

Reduce the expression by cancelling the common factors.

Cancel the common factor.

Divide by to get .