Problem : For which values of x does the function f (x), with graph shown below, fail to be continuous? differentiable?
Problem : For which values of x does the function f (x) with the following graph have f'(x) = 0?
Problem : Let f (x) = x1/3, a function defined on the entire real line. Is f differentiable at x = 0?No, the tangent to the graph at x = 0 is vertical, with undefined slope.
Problem : Let f (x) = sin(x). For which values of x is f'(x) = 0?We have f'(x) if and only if the tangent line to the graph of f (x) at x is a horizontal line. This occurs whenever sin(x) = ±1. Thus f'(x) = 0 for x = Π/2 + kΠ, where k is any integer.
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