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Calculus

Suppose that f is a differentiable function with derivative
๐‘“'(๐‘ฅ) = (๐‘ฅ โˆ’ 3)(๐‘ฅ + 1)(๐‘ฅ + 5). Determine the intervals of x for which the function of f is increasing and decreasing.

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  1. since f'(x) =0 at x = -5, -1, 3 f' changes sign there.
    Since f'(-6) < 0,
    f is increasing (f' > 0) in (-5,-1) and (3,โˆž)
    f is decreasing on (-โˆž,-5) and (-1,3)

    This is just Algebra II. Recall what you know about the properties of polynomials.

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    oobleck

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