Jessica S.

# Find the average or mean slope of the function on this interval

Consider the function f(x)=2√x +1 on the interval [2,7].  Find the average or mean slope of the function on this interval.
By the mean value theorem, we know there exists a c in the open interval (2,7) such that f'(c) is equal to this mean slope. For this problem, there is only one c that works. Find it.

## 2 Answers By Expert Tutors

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Knowledgeable and Passionate University of Pennsylvania Math Tutor

Dalia S.

it is very clear however i still seem to be getting the wrong answer, what was the final answer in your calculations?
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06/19/14 Suneil P.

f'(x)=1/sqrt(x)=avg slope=2(sqrt(7)-sqrt(2))/5

solve for x...it may be more presentable to round and use calculator at this point, unless the questions asks for exact answer.
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06/19/14

Dalia S.

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06/20/14 Suneil P.

Dalia, here is my work:

average slope=[(2√7+1)-(2√2+1)]/(7-2)

the derivative of the function 2x1/2 +1 is 2*(1/2)*x-1/2 = 1/√x

So equating the two, we have 1/sqrt(x)=2(sqrt(7)-sqrt(2))/5

Please tell me if you have a doubt on these steps.
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06/20/14 Suneil P.

note that the equation must then be solved for x; the solution represents the "c" value such that the derivative of the function at c is equivalent to the average slope over the interval
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06/20/14

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