## Jgeurts 2 years ago 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

1. Jgeurts

Anyone?

2. across

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?

3. Jgeurts

Haha that was beautiful, thank you