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Jgeurts
 3 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
Jgeurts
 3 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

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across
 3 years ago
Best ResponseYou've already chosen the best response.3The 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?

Jgeurts
 3 years ago
Best ResponseYou've already chosen the best response.0Haha that was beautiful, thank you
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