Calculus

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Find the intervals of increase and decrease for the following function:

y=x√((x-1)^4)
y'=[(4-x)^(1/2)]+(1/2)((4-x)^(-1/2))(-1)(x)
y'=[(4-x)^(1/2)]-(1/2x)((4-x)^(-1/2))
y'=((4-x)^(-1/2))[((4-x)^-1)-1/2x]

I've already factored it, how come the zeros of the derivative aren't 4 and 0?

  • Calculus -

    If I interpret your first line correctly it is
    y = x√((x-1)^4)
    Isn't that
    y = x(x-1)^2 ??
    then
    y' x(2)(x-1) + (x-1)^2
    = (x-1)(2x - x + 1)
    = (x-1)(x+1)
    = 0
    so x = 1 or x = -1 are the zeros of the derivative.


    I don't see where the (4-x)'s in your second line come from, there wasn't even a 4-x in the equation.

  • Calculus -

    Whoops, I combined 2 questions together.
    The question is y=x√(4-x).

  • Calculus -

    So what did you get for you factored derivative set equal to zero ?
    Mine was -(1/2)(4-x)^(-1/2)(3x-8) = 0
    x = 8/3

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