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

Printable View

- Nov 6th 2006, 11:31 AMbobby77mean 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

- Nov 6th 2006, 11:39 AMJameson
So $\displaystyle \frac{f(b)-f(b)}{b-a} \le -5$ for some a,b.

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

Take it from here.