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#