What is the value of c for which the instantaneous rate of change of f at #x=c# is the same as the average rate of change f over [1,4] if #f(x)=x+lnx#?

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Answer 1 · 2015-03-27T16:00:15

#c=3/ln4#

#f(x)=x+lnx#

Average rate of change over #{1, 4}# is:

#(Delta f)/(Delta x)=(f(4)-f(1))/(4-1)=(4+ln4-(1+ln1))/3=(3+ln4)/3#

#f'(x)=1+1/x#

#c# is the solution to
#1+1/x=(3+ln4)/3#

#1/x = ln4 / 3#

#x= 3/ ln4#