Question
Find the linearization L(x) of the function g(x) = xf(x^2) at x = 2 given the following information. f(2)=1 f'(2)=8 f(4)=4 f'(f)=-3
L(x)=
L(x)=
Answers
Steve
g'(x) = f(x^2) + xf'(x^2)(2x)
= f(x^2) + 2x^2 f'(x^2)
So, at x=2,
g'(2) = f(4) + 8f'(4) = 4+8(-3) = -20
g(2) = 2f(4) = 8
So, now we have a point and a slope:
L(x) = -20(x-2) + 8 = -20x+48
= f(x^2) + 2x^2 f'(x^2)
So, at x=2,
g'(2) = f(4) + 8f'(4) = 4+8(-3) = -20
g(2) = 2f(4) = 8
So, now we have a point and a slope:
L(x) = -20(x-2) + 8 = -20x+48