[11] If the function f(x) is differentiable at r = c show that there exists a positive constant A and a 6 > 0 such that If(x) - f(c)| 0 for some x ( [a, b], then fo f > 0. b. If f is continuous on [a, b] and ( fg = 0 for all continuous g on [a, b], then f = 0