# Calculus Examples

Find the Difference Quotient
Consider the difference quotient formula. Use this formula to solve for the slope of the secant line .
Find the components of the definition.
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.
Simplify .
Use the power rule to combine exponents.
Simplify .
Use the power rule to combine exponents.
Reorder and .
The final answer is .
Find the components of the definition.
Plug in the components.
Simplify.
Simplify the numerator.
Apply the distributive property.
Multiply by .
Remove parentheses.
Subtract from .