anonymous
  • anonymous
H-E-L-P Determine the extrema of below on the given interval f(x)=5x^3-61x^2+16x+3 (a) on [0,4] The minimum is ?? and the maximum is ?? (b) on [-9,9] The minimum is ?? and the maximum is ?? please solve so i can know which answer i got wrong.
Calculus1
chestercat
  • chestercat
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anonymous
  • anonymous
Do you know the derivative?
anonymous
  • anonymous
yes i did everything. x= 2/15 and x= 8
anonymous
  • anonymous
those are the critical points.

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anonymous
  • anonymous
left end point: f(0)= 3 critical points: x= 2/15 f(2/15)= 4.06074 x=8 f(8)= -1213 Right Point: f(4)= -589
anonymous
  • anonymous
Okay you don't consider \(f(8)\) for the \([0,4]\) interval..
anonymous
  • anonymous
oh......
anonymous
  • anonymous
It's apparent that \(f(2/15)\) is the maximum.
anonymous
  • anonymous
And the minimum is going to be \(f(4)\)
anonymous
  • anonymous
just 2/15? or do we write that the max as: 4.06074
anonymous
  • anonymous
so the min has to be: -589
anonymous
  • anonymous
I said \(f(2/15)\) which is equal to \(4.06074\)
anonymous
  • anonymous
okay. then what's the minimum
anonymous
  • anonymous
Now you just need to check 9 and -9 for the other interval.
anonymous
  • anonymous
since i can't use f(8)
anonymous
  • anonymous
For the \([0,4]\) interval, the minimum is -589 right?
anonymous
  • anonymous
i think so...
anonymous
  • anonymous
For the \([-9,9]\) interval... you can consider \(f(8)\), but you also need to consider \(f(-9)\) and \(f(9)\)
anonymous
  • anonymous
after i do all the work, the problem is i don't know how to pick the min and max.
anonymous
  • anonymous
for f(-9)= -8727 and for f(9) = -1149.
anonymous
  • anonymous
Is this correct ?? (a) on [0,4] The minimum is -589 and the maximum is 4.06074 (b) on [-9,9] The minimum is -8727 and the maximum is -1149
anonymous
  • anonymous
Yeah... the minimum is the LOWEST value the maximum is the HIGHEST value.
anonymous
  • anonymous
You only have to consider the values at critical points and endpoints.
anonymous
  • anonymous
i submitted this as my answer but it says its wrong. :(
anonymous
  • anonymous
You must be doing it wrong then... somehow.
anonymous
  • anonymous
i know that's why im asking you if the answer i had up there are correct.
anonymous
  • anonymous
What's your derivative?
anonymous
  • anonymous
15x^2-122x+16
anonymous
  • anonymous
can you get back to me with answer so i can see if its correct. i dont want to go step by step if its wrong in the end. i tried this problem several times...

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