How do you find the number c that satisfies the conclusion of the Mean Value Theorem for the function #f(x) = ln x# on the interval [1,7]?

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Answer 1 · 2016-09-21T19:30:32

Solve #f'(x) = (f(7)-f(1))/(7-1)# every solution in #(1,7)# is a value of #c# in the conclusion of MVT.

#f'(x) = 1/x# and #f(1)=ln1 = 0#, so we need to solve

#1/x = ln7/6#

#x = 6/ln7#.

The function does satisfy the hypotheses and there is only one solution, so we don't need to worry about it being outside the interval.