anonymous
  • anonymous
Calculus!
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
if \[f(x)=\frac{ 1 }{ 3 }x ^{3}-4x ^{2}+12x-5\] and the domain is the set of all x such that \[0\le x \le9\], then the absolut emaximum value of the function f occurs when x is.....
anonymous
  • anonymous
my teacher gave me the answer, and the answer is 9.
anonymous
  • anonymous
and haha yes i figured out how to do the last one :)

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zepdrix
  • zepdrix
So we're closed within a small interval. To find max and min, we'll do a couple things. We'll take the derivative of \(f\) to find critical points. Then we simply plug those points into the original function to see which gives us the biggest answer. But we ALSO have to plug in the END POINTS x=0 and x=9, and compare those values as well. The biggest output will be our answer.
anonymous
  • anonymous
ah , ok. because I found the derivative, and 9 was not one of the values i got when i set the derivative equal to zero and solved for x. but thank you! I didnt know that you have to include the endpoints :p
zepdrix
  • zepdrix
ya c; good times.

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