Find the linearization L(x) of the function at a.
f(x) = x⁴ + 2x², a = -1, L(x) =

Solution:

Linearization is an effective method for approximating the output of a function at any point based on the value and slope of the function, given that is differentiable on (or ) and that is close to.

The given function is f(x) = x⁴ + 2x²

We have to find L(x) at a = -1

f(-1) = 1 + 2 = 3

f’(x) = 4x³ + 4x

f’(-1) = 4(-1)³ + 4(-1)

f’(-1) = -4 - 4 = -8

The tangent line has the slope point form

y - f(-1) = f’(-1)(x + 1)

y - 3 = -8(x + 1)

y = 3 - 8(x + 1)

Therefore, the linearization L (x) is y = 3 - 8(x + 1).

Find the linearization L(x) of the function at a.
f(x) = x⁴ + 2x², a = -1, L(x) =

Summary:

The linearization L(x) of the function at a is y = 3 - 8 (x + 1).