## mathcalculus Group Title 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. one year ago one year ago

1. mathcalculus Group Title

can someone please tell me the correct answer to this. it seems like one of my answers is incorrect.

2. satellite73 Group Title

check $$f(0), f(4)$$ and also find the critical point and find $$f$$ of that number

3. mathcalculus Group Title

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

4. satellite73 Group Title

the derivative is $$15 x^2-122 x+16$$

5. satellite73 Group Title

which, by some miracle factors as $$(x-8) (15 x-2)$$

6. satellite73 Group Title

zeros of the derivative are $$\frac{2}{15}$$ and $$8$$

7. satellite73 Group Title

so $$\frac{2}{15}$$ is the $$x$$ coordinate of the local max and $$8$$ is the $$x$$ coordinate of the local min

8. mathcalculus Group Title

so for the intervals [0,4] max is: 2/15 and 8 is the min? what about [-9,9]

9. mathcalculus Group Title

i just want to make sure because it submitted the answer and it keeps saying its wrong.

10. mathcalculus Group Title

@satellite73

11. mathcalculus Group Title

any one! this is important!

12. mathcalculus Group Title

never mind! i found it. thanks to those who actually helped.

13. Peter14 Group Title

f'(x)=10x^2 - 122x +16 0=10x^2 - 122x + 16 (just working here because I don't have paper handy)

14. satellite73 Group Title

careful here the max is the $$y$$ value not the $$x$$ value

15. Peter14 Group Title

just finding critical points

16. Peter14 Group Title

oh, sorry you already found them

17. satellite73 Group Title

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

18. satellite73 Group Title

for $$[-9,9]$$ you need to check $f(-9),f(\frac{2}{15}), f(8), f(9)$

19. mathcalculus Group Title

got it. thank you!

20. satellite73 Group Title

yw