If f'(x) > 3 for all x and f(2)= 5,

Question

what can you conclude about f(4)?

Answer 1

By the Mean Value Theorem, there exists at least one number, c, in the interval (2,4) so that

f'(c) = [f(4) - f(2)] / (4 - 2)

Since f'(c) > 3 and f(2) = 5, we have (f(4) - 5) / 2 > 3.

So, f(4) > 11.

Answer 2

Since the first derivative is always positive, the function is always increasing.

f(4) > f(2)