Question

If f(-1) = -3 and f'(x)= (4x^2)/(x^3 +3) , which of the following is the best approximation for f(-1.1) using local linearization?

a. -7.2
b. 2.8
c. -1.2
d. -3.2

Answer 1

Linear approximation equation is
f(x)=f(a)+f'(a)(x-a)
f(-1.1)=f(-1)+f'(-1)(-1.1-(-1))
f(-1.1)=-3+2(-1.1+1)=-3-0.2=-3.2