anonymous
  • anonymous
H-E-L-P so frustrating!! 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
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
can someone please tell me the correct answer to this. it seems like one of my answers is incorrect.
anonymous
  • anonymous
check \(f(0), f(4)\) and also find the critical point and find \(f\) of that number
anonymous
  • anonymous
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

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More answers

anonymous
  • anonymous
the derivative is \( 15 x^2-122 x+16\)
anonymous
  • anonymous
which, by some miracle factors as \((x-8) (15 x-2)\)
anonymous
  • anonymous
zeros of the derivative are \(\frac{2}{15}\) and \(8\)
anonymous
  • anonymous
so \(\frac{2}{15}\) is the \(x\) coordinate of the local max and \(8\) is the \(x\) coordinate of the local min
anonymous
  • anonymous
so for the intervals [0,4] max is: 2/15 and 8 is the min? what about [-9,9]
anonymous
  • anonymous
i just want to make sure because it submitted the answer and it keeps saying its wrong.
anonymous
  • anonymous
@satellite73
anonymous
  • anonymous
any one! this is important!
anonymous
  • anonymous
never mind! i found it. thanks to those who actually helped.
anonymous
  • anonymous
f'(x)=10x^2 - 122x +16 0=10x^2 - 122x + 16 (just working here because I don't have paper handy)
anonymous
  • anonymous
careful here the max is the \(y\) value not the \(x\) value
anonymous
  • anonymous
just finding critical points
anonymous
  • anonymous
oh, sorry you already found them
anonymous
  • anonymous
8 is not in the interval \([0,4]\) for that one, you need to check \(f(0), f(4), f(\frac{2}{15})\) the largest is the max and the smallest is the min
anonymous
  • anonymous
for \([-9,9]\) you need to check \[f(-9),f(\frac{2}{15}), f(8), f(9)\]
anonymous
  • anonymous
got it. thank you!
anonymous
  • anonymous
yw

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