Assume f is differentiable and has just one critical point, at x = 3. You are given additional conditions. In each case decide whether x = 3 is a local maximum, a local minimum, or neither. You should be able to sketch possible graphs for all four cases. f '(1) = 4 and f '(8) = --4
x = 3 is a local maximum.
x = 3 is a local minimum
x = 3 is neither a local maximum nor a local minimum.