# Calculus Examples

,

Step 1

Consider the function used to find the linearization at .

Step 2

Substitute the value of into the linearization function.

Step 3

Step 3.1

Replace the variable with in the expression.

Step 3.2

Simplify .

Step 3.2.1

Remove parentheses.

Step 3.2.2

Add and .

Step 4

Step 4.1

By the Sum Rule, the derivative of with respect to is .

Step 4.2

Differentiate using the Power Rule which states that is where .

Step 4.3

Since is constant with respect to , the derivative of with respect to is .

Step 4.4

Add and .

Step 5

Substitute the components into the linearization function in order to find the linearization at .

Step 6

Step 6.1

Multiply by .

Step 6.2

Subtract from .

Step 7