If f(3) = 11 and f '(x) ≥ 3 for 3 ≤ x ≤ 5, how small can f(5) possibly be?

Answer 1

Since f'(x) ≥ 3, ∫_{(from 3 to 5)} f'(x)dx ≥ ∫_{(from 3 to 5)} 3dx.

So, f(5) - f(3) ≥ 6

f(5) - 11 ≥ 6

Thus, f(5) ≥ 17