Suppose f(x) is continuous on [4,8] and −4 is less than or equal to (f'(x) that is less than or equal to 5 for all x in (4,8). Use the Mean Value Theorem to estimate f(8)−f(4).

ANSWER

Question

Suppose f(x) is continuous on [4,8] and −4 is less than or equal to (f'(x) that is less than or equal to 5 for all x in (4,8). Use the Mean Value Theorem to estimate f(8)−f(4).

ANSWER < or = f(8)-f(4) < or = ANSWER

anonymous · Answer

Anyone?

across · Answer

The mean value theorem tells you that there is a $c$ in $(4,8)$ such that$$f'(c)=\frac{f(8)-f(4)}4.$$Moreover, you're told that $-4\leqslant f'(x)\leqslant5$ for all $x$ in $(4,8)$. Thereore$$-4\leqslant\frac{f(8)-f(4)}4\leqslant5,\-16\leqslant f(8)-f(4)\leqslant20.$$Easy?

anonymous · Answer

Haha that was beautiful, thank you