Question

Let f be the function defined by f(x) = x + ln x. 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 of f over [1,4]?

Answer 1

f'(x) = 1 + 1/x
so you want c such that
1 + 1/c = (f(4)-f(1))/(4-1)