# Math Help - mean value

1. ## mean value

Suppose that f (0)= - 3 and f ' (x) <= -5 for all values of x. The inequality gives restriction on rate of growth of f. which then imposes a restriction on possible values of f. Use mean value theorem to determine how large f (4) can possible be

2. So $\frac{f(b)-f(b)}{b-a} \le -5$ for some a,b.

Thus $\frac{f(b)-(-3)}{4-0} \le -5$

Take it from here.