Question

If f(2) = 13 and f '(x) ≥ 3 for 2 ≤ x ≤ 4, how small can f(4) possibly be?

Answer 1

The slope f'(x) = [f(4) - f(2)]/(4-2)≥3,
so [f(4) - 13]/2 ≥3
f(4) -13 ≥ 6
f(4)≥19, so it can be as small as 19.