Suneil P. answered • 06/19/14
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Def'n of avg slope: http://demo.activemath.org/ActiveMath2/search/show.cmd?id=mbase://LeAM_calculus/diffquot/def_average_slope
To find the "c" value from the MVT, simply take the derivative of the function and set it equal to the average slope; solving this equation would yield all the "c" values.
Besides the correct answer, is it clear what we are doing and why?
Hope this helps!
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.
your answer is incorrect
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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
Dalia S.
06/19/14