Calculus

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1. For the function f(x)=4x^3-30x^2+4:
a) Find the critical numbers of f(if any);
b) Find the open intervals where the function is increasing or decreasing; and
c) Apply the First Derivative Test to identify all relative extrema
2. For the function f(x)=(x-1)^(8/11)
a) Find the critical numbers of f(if any);
b) Find the open intervals where the function is increasing or decreasing; and
c) Apply the First Derivative Test to identify all relative extrema

  • Calculus -

    f' = 12x^2 - 60x = 12x(x-5)

    as you know
    extrema where f'=0
    increasing where f' > 0

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