(a) Consider f(x) = px2 + qx + r be the quadratic function defined on the closed interval [a, b]. Illustrate that there is exactly one point ‘c' in (a, b) at which f satisfies conclusion of Mean Value theorem.
(b) For functions f(x) =x4 - 4x3 + 4x2 and g(x)= x2/3(x2-4), determine (a) Interval on which function is increasing and decreasing (b) Functions' local and absolute extreme values.