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What is the state of the function f at x = 2?

F(x) = [x^3 for x < 2; 5x - 2 for x > or = to 2]

?continuous or differentiable both or neither one or the other?

  • Calculus -

    F(x) is continuous at x=2, since
    2^3 = 5*2-2 = 8

    But, F' is not continuous, since
    3*2^2 = 12
    5 = 5

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