mathcalculus
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.
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wio
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Do you know the derivative?
mathcalculus
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yes i did everything. x= 2/15 and x= 8
mathcalculus
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those are the critical points.
mathcalculus
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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
wio
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Okay you don't consider \(f(8)\) for the \([0,4]\) interval..
mathcalculus
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oh......
wio
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It's apparent that \(f(2/15)\) is the maximum.
wio
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And the minimum is going to be \(f(4)\)
mathcalculus
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just 2/15? or do we write that the max as: 4.06074
mathcalculus
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so the min has to be: -589
wio
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I said \(f(2/15)\) which is equal to \(4.06074\)
mathcalculus
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okay. then what's the minimum
wio
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Now you just need to check 9 and -9 for the other interval.
mathcalculus
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since i can't use f(8)
wio
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For the \([0,4]\) interval, the minimum is -589 right?
mathcalculus
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i think so...
wio
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For the \([-9,9]\) interval... you can consider \(f(8)\), but you also need to consider \(f(-9)\) and \(f(9)\)
mathcalculus
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after i do all the work, the problem is i don't know how to pick the min and max.
mathcalculus
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for f(-9)= -8727 and for f(9) = -1149.
mathcalculus
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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
wio
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Yeah... the minimum is the LOWEST value the maximum is the HIGHEST value.
wio
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You only have to consider the values at critical points and endpoints.
mathcalculus
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i submitted this as my answer but it says its wrong. :(
wio
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You must be doing it wrong then... somehow.
mathcalculus
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i know that's why im asking you if the answer i had up there are correct.
wio
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What's your derivative?
mathcalculus
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15x^2-122x+16
mathcalculus
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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...