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Math Help - increasing or decreasing function

  1. #1
    Senior Member euclid2's Avatar
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    increasing or decreasing function

    for f(x)=x^4-32x+4 find where f'(x)=0, the intervals for which the function increase and decrease, and all the local extrema
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    Quote Originally Posted by euclid2 View Post
    for f(x)=x^4-32x+4 find where f'(x)=0, the intervals for which the function increase and decrease, and all the local extrema
    Hi euclid2,

    f'(x)=4x^3-32

    f'(x)=0\ \Rightarrow\ x^3=\frac{32}{4}=8\ \Rightarrow\ x=2

    f''(x)=12x^2

    This is positive when x=2, hence it is a minimum
    and since there is only one solution for the derivative f'(x)=0, it is the only turning point and therefore the absolute minimum,
    there are no local maxima.

    f''(x)=0 at x=0, but is always positive otherwise, so the graph is concave up.
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