What is the value of c for which

Payton Benson

Payton Benson

Answered question

2022-03-13

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?

Answer & Explanation

Cohen Hunt

Cohen Hunt

Beginner2022-03-14Added 4 answers

f(x)=x+lnx
Average rate of change over {1,4} is:
fx=f(4)f(1)41=4+ln4(1+ln1)3=3+ln43
f(x)=1+1x
c is the solution to
1+1x=3+ln43
1x=ln43
x=3ln4

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