The Mean Value Theorem requires that f be continuous on [1, 4] and differentiable on (1, 4). This is true because ln(x) is differentiable for x>0.

c mentioned is a number from (1, 4) such that f'(c)=(f(4)-f(1))/(4-1)=ln(4)/3.

f'(c)=1/c and = ln(4)/3, so `c=3/ln(4) approx 2.16.`