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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?

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  1. myininaya
    • 5 years ago
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    \[\frac{d^2([f(x)]^3)}{dx^2}\] \[=\frac{d}{dx}(3[f(x)]^2f'(x))=3[2f(x)f'(x)f'(x)+[f(x)]^2f''(x)]\]

  2. myininaya
    • 5 years ago
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    \[3[f(2)f'(2)f'(2)+[f(2)]^2f''(2)]\]

  3. myininaya
    • 5 years ago
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    now plug in and evaluate and simplify

  4. anonymous
    • 5 years ago
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    Thank you I'm going to try it now.

  5. myininaya
    • 5 years ago
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    I used chain rule and product rule by the way

  6. anonymous
    • 5 years ago
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    okay :)

  7. anonymous
    • 5 years ago
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    The answers I keep coming up don't seem correct. Can you please explain in more detail.

  8. myininaya
    • 5 years ago
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    lol and I didn't notice you were having problems with this money sorry

  9. amistre64
    • 5 years ago
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    just like a woman, they state their opinions and then yougotta live with em ;)

  10. myininaya
    • 5 years ago
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    \[3[6(-4)(-4)+(6)^2(2)]=3[6(16)+36(2)]=3[96+72]=3[168]\]

  11. myininaya
    • 5 years ago
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    = 504 is what I'm getting

  12. amistre64
    • 5 years ago
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    ipso facto

  13. anonymous
    • 5 years ago
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    I was missing the 2 in front of the f(x). But I understand now.

  14. amistre64
    • 5 years ago
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    i dont think id of come to that today;

  15. myininaya
    • 5 years ago
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    lol poor amistre do you ever come to it? ;)

  16. anonymous
    • 5 years ago
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    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
    • 5 years ago
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    \[V(t)=\frac{4}{3} \pi [r(t)]^3=> V'(t)=\frac{4}{3} \pi 3 [r(t)]^2 r'(t)\]

  18. myininaya
    • 5 years ago
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    \[\S(t)=4 \pi [r(t)]^2 => \S'(t)=4 \pi 2r(t) r'(t)=8 \pi r(t)r'(t)\]

  19. myininaya
    • 5 years ago
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    \[V'(t)=4 [r(t)]^2 r'(t)\]

  20. myininaya
    • 5 years ago
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    so r'=2 do you see that in the first sentence?

  21. myininaya
    • 5 years ago
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    \[V=36 \pi\] from second sentence

  22. myininaya
    • 5 years ago
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    we want to know S' based on second sentence

  23. myininaya
    • 5 years ago
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    \[36=\frac{4}{3} \pi r^3\] solve this for r

  24. myininaya
    • 5 years ago
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    to find S' this is the only thing we need since r' is already given

  25. myininaya
    • 5 years ago
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    oops the V=36 pi

  26. myininaya
    • 5 years ago
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    \[36 \pi =\frac{4}{3} \pi r^3\] *

  27. myininaya
    • 5 years ago
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    solve that for r

  28. anonymous
    • 5 years ago
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    So am I suppose to divide both sides by 4/3\[\pi\] ?

  29. myininaya
    • 5 years ago
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    or multiply both sides by 3/(4pi)

  30. anonymous
    • 5 years ago
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    so would I have 27pi=r^3?

  31. myininaya
    • 5 years ago
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    well the pi's would cancel

  32. anonymous
    • 5 years ago
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    27=r^3?

  33. myininaya
    • 5 years ago
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    yes since pi/pi=1 so r=3

  34. myininaya
    • 5 years ago
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    \[\S'=8 \pi r r'\]

  35. myininaya
    • 5 years ago
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    and remember r'=2

  36. myininaya
    • 5 years ago
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    So now you can find S'

  37. anonymous
    • 5 years ago
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    So I should come up with 48pi cm^2/sec correct?

  38. myininaya
    • 5 years ago
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    48 pi is right!

  39. anonymous
    • 5 years ago
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    Thanks!!

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