Given the function # f(x)=1/sqrt(x+2)#, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [-1,23] and find the c?

1 Answer
Jim H
Nov 7, 2016

Answer the questions: Is #f# continuous on the closed interval? Is it differentiable on the open interval? Solve #f'(x) = (f(23)-f(-1))/(23-(-1))# in the open interval.

Explanation:

The function is continuous on ites domain #[-2,oo)#, so the first answer is, Yes.

#f'(x) = -1/sqrt(x+2)^3# which exists for all #x > -2#. So the second answer is, Yes.

The only solution to

#-1/sqrt(x+2)^3 = (1/5-1)/24#

is #x=-2+30^(2/3)# which is in the open interval. So that is #c#.

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