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.

- anonymous

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- anonymous

Do you know the derivative?

- anonymous

yes i did everything. x= 2/15 and x= 8

- anonymous

those are the critical points.

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## More answers

- 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

Okay you don't consider \(f(8)\) for the \([0,4]\) interval..

- anonymous

oh......

- anonymous

It's apparent that \(f(2/15)\) is the maximum.

- anonymous

And the minimum is going to be \(f(4)\)

- anonymous

just 2/15? or do we write that the max as: 4.06074

- anonymous

so the min has to be: -589

- anonymous

I said \(f(2/15)\) which is equal to \(4.06074\)

- anonymous

okay. then what's the minimum

- anonymous

Now you just need to check 9 and -9 for the other interval.

- anonymous

since i can't use f(8)

- anonymous

For the \([0,4]\) interval, the minimum is -589 right?

- anonymous

i think so...

- anonymous

For the \([-9,9]\) interval... you can consider \(f(8)\), but you also need to consider \(f(-9)\) and \(f(9)\)

- anonymous

after i do all the work, the problem is i don't know how to pick the min and max.

- anonymous

for f(-9)= -8727 and for f(9) = -1149.

- 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

Yeah... the minimum is the LOWEST value the maximum is the HIGHEST value.

- anonymous

You only have to consider the values at critical points and endpoints.

- anonymous

i submitted this as my answer but it says its wrong. :(

- anonymous

You must be doing it wrong then... somehow.

- anonymous

i know that's why im asking you if the answer i had up there are correct.

- anonymous

What's your derivative?

- anonymous

15x^2-122x+16

- 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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