Mean Value Theorem

Question

Suppose that f(0) = 3 and f'(x) < 4 for all values of x. Use the Mean Value Theorem to determine how large f(4) can possibly be.

Answer: f(4) < 3

Answer 1

I don't see how we can arrive at f(4) < 3.

The Mean Value Theorem states that

there is some value c on (0,4) such that

If f(0) = 3 and f’(x) < 4 for all x, this means that

So f(4) – 3 < 16 and we have

Answer: f(4) < 19