Please explain thoroughly with all steps

Question 5 a) Find a, positive real number, such that the Mean Value Theorem of Integrals holds on [1, e 1] of 2 x2, x <_: f a x>0 x+1 b) Find It, positive real number, such that the function 2 f(x) =x3+x has average favg = S on [0, 1:]. Then, nd 6 such that f (c) = favg