# Derivative question calculus

How would I figure out the following question.

Find the values of x at which the rate of change of $y=30+28x^2+16x^3-2x^4$ with respect to $x$ is zero.

Do I have to take the derivative and set it to zero or something else.

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Yes ${}{}{}{}{}{}{}{}$ –  Amr Feb 10 '13 at 17:44
Yes, the rate of change is the derivative, so you gotta set the derivative equal to zero. –  ciceksiz kakarot Feb 10 '13 at 17:44
Hmm but how many times would I take derivative only one time or several times. –  Fernando Martinez Feb 10 '13 at 17:47
Just like ciceksizkakarot said ... –  Hagen von Eitzen Feb 10 '13 at 17:54

The first derivative is the same thing as the rate of change, so the question essentially says to find when the first derivative equals zero. So you have $$\frac {dy} {dx} = -8x(x-7)(x+1) = 0,$$ so the x-coordinates where the rate of change is zero are $x = 0, 7,$ and $-1$.