Let f: [a, b] → r be a continuous function. let ε > 0 be a constant. for x [a + e, b-el, define g(x) : = (a) show that g is differentiable and find the derivative. (b) let f be differentiable and fix x e (a, b) (lete be small enough). what happens to g'(x) as ε gets smaller? (c) find g for f(x) : = lxle = 1 (you can assume [a, b] is large enough).