Calculus 1 Linearization Question

Question

Find the linearization L(x) of the function g(x)=xf(x2) at x=2 given the following information.

f(2)=0 f′(2)=12 f(4)=6 f′(4)=−2

Answer 1

g(2) = 2f(4) = 12; g'(x) = f(x²) + f'(x²)·2x²; g'(2) = f'(4)·2·4 = - 16;

L(x) = g(2) + g'(2)(x - 2); L(x) = 12 - 16(x - 2); L(x) = - 16x + 44