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Suppose that 3\leq f'(x) \leq 5 for all values of x. Show that 18\leq f(8)-f(2) \leq 30.

Question:

Suppose that {eq}3\leq f'(x) \leq 5 {/eq} for all values of x. Show that {eq}18\leq f(8)-f(2) \leq 30 {/eq}.

Mean Value Theorem:

Assume that f is a function differentiable on a closed bounded real interval. Then the slope of the secant line connecting the endpoints of the graph of the function on this interval is equal to the slope of the tangent line to the graph for some point in the interval.

Answer and Explanation:

Assume that {eq}\; f(x) \; {/eq} is differentiable on the real interval {eq}\; [2, \, 8] \; {/eq} and {eq}\; 3\leq f'(x) \leq 5 \; {/eq} for...

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What is the Mean Value Theorem?

from Math 104: Calculus

Chapter 8 / Lesson 3
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