Question

Find the linearization L(x) of the function at a.
1. F(x)=x^(3/4), a=16

Answer 1

L(x)=F(a) + F'(a)*(x-a)
F(a)=16^(3/4)
F'(x)=3(x^(-1/4))/4
F'(a)=3/4 * 16^(-1/4)

L(x)=16^(3/4) + (3/4 * 16^(-1/4))(x-16)
L(x)=8+(3/8)(x-16)