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# Find the linearization L(x) of the function at a.

f(x) = x^{4} + 2x^{2}, 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) = x^{4} + 2x^{2}

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

f(-1) = 1 + 2 = 3

f’(x) = 4x^{3} + 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) = x^{4} + 2x^{2}, a = -1, L(x) =

**Summary:**

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

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