## anonymous 5 years ago If f(2)=6, f'(2)=-4, and f"(2)=2, what is (d^2*(f^3 (x)))/(dx^2 ) at x=2?

1. myininaya

$\frac{d^2([f(x)]^3)}{dx^2}$ $=\frac{d}{dx}(3[f(x)]^2f'(x))=3[2f(x)f'(x)f'(x)+[f(x)]^2f''(x)]$

2. myininaya

$3[f(2)f'(2)f'(2)+[f(2)]^2f''(2)]$

3. myininaya

now plug in and evaluate and simplify

4. anonymous

Thank you I'm going to try it now.

5. myininaya

I used chain rule and product rule by the way

6. anonymous

okay :)

7. anonymous

The answers I keep coming up don't seem correct. Can you please explain in more detail.

8. myininaya

lol and I didn't notice you were having problems with this money sorry

9. amistre64

just like a woman, they state their opinions and then yougotta live with em ;)

10. myininaya

$3[6(-4)(-4)+(6)^2(2)]=3[6(16)+36(2)]=3[96+72]=3[168]$

11. myininaya

= 504 is what I'm getting

12. amistre64

ipso facto

13. anonymous

I was missing the 2 in front of the f(x). But I understand now.

14. amistre64

i dont think id of come to that today;

15. myininaya

lol poor amistre do you ever come to it? ;)

16. anonymous

The radius of a sphere is increasing at a constant rate of 2cm/sec. At the instant when the volume of the sphere is 36π cm^3, what is the rate that the surface area is increasing? Surface area=4π r^2 Volume=4/3π r^3 This one I need a full full explanation on

17. myininaya

$V(t)=\frac{4}{3} \pi [r(t)]^3=> V'(t)=\frac{4}{3} \pi 3 [r(t)]^2 r'(t)$

18. myininaya

$\S(t)=4 \pi [r(t)]^2 => \S'(t)=4 \pi 2r(t) r'(t)=8 \pi r(t)r'(t)$

19. myininaya

$V'(t)=4 [r(t)]^2 r'(t)$

20. myininaya

so r'=2 do you see that in the first sentence?

21. myininaya

$V=36 \pi$ from second sentence

22. myininaya

we want to know S' based on second sentence

23. myininaya

$36=\frac{4}{3} \pi r^3$ solve this for r

24. myininaya

to find S' this is the only thing we need since r' is already given

25. myininaya

oops the V=36 pi

26. myininaya

$36 \pi =\frac{4}{3} \pi r^3$ *

27. myininaya

solve that for r

28. anonymous

So am I suppose to divide both sides by 4/3$\pi$ ?

29. myininaya

or multiply both sides by 3/(4pi)

30. anonymous

so would I have 27pi=r^3?

31. myininaya

well the pi's would cancel

32. anonymous

27=r^3?

33. myininaya

yes since pi/pi=1 so r=3

34. myininaya

$\S'=8 \pi r r'$

35. myininaya

and remember r'=2

36. myininaya

So now you can find S'

37. anonymous

So I should come up with 48pi cm^2/sec correct?

38. myininaya

48 pi is right!

39. anonymous

Thanks!!