# Calculus Examples

,
Find and evaluate at and to find the slope of the tangent line at and .
Simplify .
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 .
Move to the left of .
Multiply by .
Differentiate both sides of the equation.
The derivative of with respect to is .
Differentiate the right side of the equation.
Differentiate.
By the Sum Rule, the derivative of with respect to is .
Differentiate using the Power Rule which states that is where .
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 using the Constant Rule.
Since is constant with respect to , the derivative of with respect to is .
Reform the equation by setting the left side equal to the right side.
Replace with .
Evaluate at and .
Replace the variable with in the expression.
Multiply by .
Plug in the slope of the tangent line and the and values of the point into the point-slope formula .
Simplify.
The slope-intercept form is , where is the slope and is the y-intercept.
Rewrite in slope-intercept form.
Multiply by .
Simplify .
Multiply by .
Apply the distributive property.
Multiply by .
Move all terms not containing to the right side of the equation.
Add to both sides of the equation.