Question

Find the linearization l(x) of the function at a. f(x) = x4 + 4x2, a = 1

Answer 1

The formula of linearization is

L = f(a)+f'(a)(x-a)

We have $f(x) = x^4+4x^2$

And it is given in the question that a=1.

So f(a) = f(1) = 1+4=5

Now we need to find f'(a) and for that , first we need to find f'(x).

$f'(x) = 4x^{4-1}+4(2)x^{2-1}$

$f'(x)=4x^3+8x$

At a=1,

$f'(1)= 4+8=12$

Substituting the values of f(1) and f'(1) in the linearization formula

L=5+12(x-1)

L= 5+12x-12

L= 12x -7

And that's the required linearization .