How do you find the linearization of $f(x) = x^4 + 5x^2$ at a=-1?

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Answer 1 · 2018-04-18T18:39:49

$L(x)=-6x$

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

We're given $a=-1, f(x)=x^4+5x^2,$ so

$(x-a)=(x-(-1))=(x+1)$

$f(a)=f(-1)=(-1)^4+5(-1)^2=1+5=6$

$f'(x)=4x^3+10x$

$f'(a)=f'(-1)=4(-1)^3+10(-1)=4-10=-6$

Then,

$L(x)=6-6(x+1)$

$L(x)=6-6x-6$

$L(x)=-6x$

How do you find the linearization of f(x) = x^4 + 5x^2f(x) = x^4 + 5x^2 at a=-1?