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

,
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 .
Remove parentheses.
Simplify each term.
Raise to the power of .
Raise to the power of .
Multiply by .
Find the derivative and evaluate it at .
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.
Raise to the power of .
Multiply by .
Multiply by .
Subtract from .
Substitute the components into the linearization function in order to find the linearization at .
Simplify.
Simplify each term.
Apply the distributive property.
Multiply by .
Subtract from .
Find the Linearization at a=-1 f(x)=x^4+2x^2 , a=-1