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Calculus

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Find the intervals of increase and decrease for the following function

h(x)=(x^3)(x-1)^4
h'(x)=[(3x^2)(x-1)^4]+(4x^3)(x-1)^3

How do I find the zeros?

Thanks.

  • Calculus -

    The zeros of the derivative or the zeros of the function ?
    I will assume you want the zeros of the derivative.

    factor it first
    = x^2(x-1)^3[4x + 3(x-1)]
    = x^2(x-1)^3(7x-3)
    we set this equal to zero to get
    x = 0, x = 1 and x = 3/7

    remember that the function increases when the first derivative is positive, and decreases when that derivative is negative.
    Can you take it from here ?

  • Calculus -

    Do you factor it by taking the lowest ^ ? I can continue from there, thanks! :)

  • Calculus -

    The answer key indicated that 0 is not a zero.

  • Calculus -

    Your question was,
    "how do I find the zeros"

    x = 0 is a solution to h(x) = 0 and h'(x) = 0

  • Calculus -

    If x=0, shouldn't it be used to determine the increase and decrease?

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