Linearization of f(x)=x^1/3 at a=-64

[Rasine]

Find the linearization of f(x)= x^1/3 at a=-64

so i am trying to use f(x)=f(a)+f'(a)(x-a)

f(a)=-4
f'(x)=1/3(x^-2/3)
f'(a)=-1/48

so i get -4+1/48(x+64)


is that right?

 

[Dick]

Well, you say f'(a)=-1/48 and you put +1/48 into the answer. Which is it?

 

[Rasine]

it is the latter

 

[Dick]

Keerect. Then everything is ok.