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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asked Feb 10, 2013 at 17:43
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3$\begingroup$ Yes ${}{}{}{}{}{}{}{}$ $\endgroup$– AmrFeb 10, 2013 at 17:44
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1$\begingroup$ Yes, the rate of change is the derivative, so you gotta set the derivative equal to zero. $\endgroup$– ciceksiz kakarotFeb 10, 2013 at 17:44
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$\begingroup$ Hmm but how many times would I take derivative only one time or several times. $\endgroup$– Fernando MartinezFeb 10, 2013 at 17:47
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$\begingroup$ Just like ciceksizkakarot said ... $\endgroup$– Hagen von EitzenFeb 10, 2013 at 17:54
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1 Answer
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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 $-1$.
