# Calculus Examples

Find the Linearization at x=6
,
Consider the function used to find the linearization at .
Substitute the value of into the linearization function.
Evaluate .
Replace the variable with in the expression.
Simplify the result.
Find the derivative and evaluate it at .
Find the derivative.
By the Sum Rule, the derivative of with respect to is .
Differentiate using the Power Rule which states that is where .
Since is constant with respect to , the derivative of with respect to is .
Replace the variable with in the expression.
Substitute the components into the linearization function in order to find the linearization at .
Simplify.
Multiply by .
Remove unnecessary parentheses.
Subtract from .