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Jgeurts
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
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?
Haha that was beautiful, thank you