Question

A differentiable function f has the property that f(5)=3 and fprime(5)=4. What is the estimate for f(4.8) using the local linear approximation for f at x=5?

Answer 1

The linear approximation means that you assume the function is linear. So, just do :
f(5) + f'(5) (x-5)

This works out, in this specific case
3 + 4 (- 0.2)

Hope this helps