## mathcalculus 2 years ago 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.

1. wio

Do you know the derivative?

2. mathcalculus

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

3. mathcalculus

those are the critical points.

4. mathcalculus

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

5. wio

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

6. mathcalculus

oh......

7. wio

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

8. wio

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

9. mathcalculus

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

10. mathcalculus

so the min has to be: -589

11. wio

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

12. mathcalculus

okay. then what's the minimum

13. wio

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

14. mathcalculus

since i can't use f(8)

15. wio

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

16. mathcalculus

i think so...

17. wio

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

18. mathcalculus

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

19. mathcalculus

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

20. mathcalculus

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

21. wio

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

22. wio

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

23. mathcalculus

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

24. wio

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

25. mathcalculus

26. wio

27. mathcalculus

15x^2-122x+16

28. mathcalculus

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...