If f(−1) = −3 and f prime of x equals the quotient of 4 times x squared and the quantity x cubed plus 3 , which of the following is the best approximation for f(–1.1) using local linearization

Answer 1

df/dx = 4 x^2/[x^3 +3]
at x = -1
df/dx = 4/[2] = 2

so
f(-1+dx) = f(-1) + 2 dx
here dx = -.1
so
f(-1-.1) = -3 +2(-.1)
= -3 -.2
=-3.2