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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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    $\begingroup$ Yes ${}{}{}{}{}{}{}{}$ $\endgroup$
    – Amr
    Feb 10, 2013 at 17:44
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    $\begingroup$ Yes, the rate of change is the derivative, so you gotta set the derivative equal to zero. $\endgroup$ Feb 10, 2013 at 17:44
  • $\begingroup$ Hmm but how many times would I take derivative only one time or several times. $\endgroup$ Feb 10, 2013 at 17:47
  • $\begingroup$ Just like ciceksizkakarot said ... $\endgroup$ Feb 10, 2013 at 17:54

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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 $-1$.

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