The Derivative

Problem : For which values of x does the function f (x) , with graph shown below, fail to be continuous? differentiable?

Figure %: Locate the Discontinuities

Problem : For which values of x does the function f (x) with the following graph have f'(x) = 0 ?

Figure %: Locate the Points for which f'(x) = 0

Problem : Let f (x) = x ^1/3 , a function defined on the entire real line. Is f differentiable at x = 0 ?

Problem : Let f (x) = sin(x) . For which values of x is f'(x) = 0 ?