By the Mean Value Theorem, we know there exists a c in the open interval (2,5) such that f′(c) is equal to this mean slope. For this problem, there is only one c that works. Find it.

Name: For the function f(x) = 8sqrt(x) + 1, find the value of c between 2 and 5, so tangent at (c, f(c))..
Uploaded: 2025-12-28T00:31:48+00:00
Description: Answer by Doug C. to By the Mean Value Theorem, we know there exists a c in the open interval (2,5) such that f′(c) is equal to this mean slope. For this problem, there is only one c that works. Find it. f(x)=8√(x)+1

Question

f(x)=8√(x)+1I find the mean or average slope its 2.1933 and I know to find C you have to take the derivative of your functionwhich is 4/√x and set it equal to 2.1933 and then solve for x. Which i did and got 3.32592, but its wrong and honestly I have no idea why.

Doug C. · Accepted Answer

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By the Mean Value Theorem, we know there exists a c in the open interval (2,5) such that f′(c) is equal to this mean slope. For this problem, there is only one c that works. Find it.

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By the Mean Value Theorem, we know there exists a c in the open interval (2,5) such that f′(c) is equal to this mean slope. For this problem, there is only one c that works. Find it.

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