,

Consider the function used to find the linearization at .

Substitute the value of into the linearization function.

Replace the variable with in the expression.

Simplify .

Remove parentheses.

Simplify each term.

One to any power is one.

One to any power is one.

Multiply by .

Add and .

Find the derivative of .

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 .

Replace the variable with in the expression.

Simplify.

Simplify each term.

One to any power is one.

Multiply by .

Multiply by .

Add and .

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

Simplify each term.

Apply the distributive property.

Multiply by .

Subtract from .

Find the Linearization at a=1 f(x)=x^4+3x^2 , a=1