anonymous
  • anonymous
If f(2)=6, f'(2)=-4, and f"(2)=2, what is (d^2*(f^3 (x)))/(dx^2 ) at x=2?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
myininaya
  • myininaya
\[\frac{d^2([f(x)]^3)}{dx^2}\] \[=\frac{d}{dx}(3[f(x)]^2f'(x))=3[2f(x)f'(x)f'(x)+[f(x)]^2f''(x)]\]
myininaya
  • myininaya
\[3[f(2)f'(2)f'(2)+[f(2)]^2f''(2)]\]
myininaya
  • myininaya
now plug in and evaluate and simplify

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anonymous
  • anonymous
Thank you I'm going to try it now.
myininaya
  • myininaya
I used chain rule and product rule by the way
anonymous
  • anonymous
okay :)
anonymous
  • anonymous
The answers I keep coming up don't seem correct. Can you please explain in more detail.
myininaya
  • myininaya
lol and I didn't notice you were having problems with this money sorry
amistre64
  • amistre64
just like a woman, they state their opinions and then yougotta live with em ;)
myininaya
  • myininaya
\[3[6(-4)(-4)+(6)^2(2)]=3[6(16)+36(2)]=3[96+72]=3[168]\]
myininaya
  • myininaya
= 504 is what I'm getting
amistre64
  • amistre64
ipso facto
anonymous
  • anonymous
I was missing the 2 in front of the f(x). But I understand now.
amistre64
  • amistre64
i dont think id of come to that today;
myininaya
  • myininaya
lol poor amistre do you ever come to it? ;)
anonymous
  • 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
myininaya
  • myininaya
\[V(t)=\frac{4}{3} \pi [r(t)]^3=> V'(t)=\frac{4}{3} \pi 3 [r(t)]^2 r'(t)\]
myininaya
  • myininaya
\[\S(t)=4 \pi [r(t)]^2 => \S'(t)=4 \pi 2r(t) r'(t)=8 \pi r(t)r'(t)\]
myininaya
  • myininaya
\[V'(t)=4 [r(t)]^2 r'(t)\]
myininaya
  • myininaya
so r'=2 do you see that in the first sentence?
myininaya
  • myininaya
\[V=36 \pi\] from second sentence
myininaya
  • myininaya
we want to know S' based on second sentence
myininaya
  • myininaya
\[36=\frac{4}{3} \pi r^3\] solve this for r
myininaya
  • myininaya
to find S' this is the only thing we need since r' is already given
myininaya
  • myininaya
oops the V=36 pi
myininaya
  • myininaya
\[36 \pi =\frac{4}{3} \pi r^3\] *
myininaya
  • myininaya
solve that for r
anonymous
  • anonymous
So am I suppose to divide both sides by 4/3\[\pi\] ?
myininaya
  • myininaya
or multiply both sides by 3/(4pi)
anonymous
  • anonymous
so would I have 27pi=r^3?
myininaya
  • myininaya
well the pi's would cancel
anonymous
  • anonymous
27=r^3?
myininaya
  • myininaya
yes since pi/pi=1 so r=3
myininaya
  • myininaya
\[\S'=8 \pi r r'\]
myininaya
  • myininaya
and remember r'=2
myininaya
  • myininaya
So now you can find S'
anonymous
  • anonymous
So I should come up with 48pi cm^2/sec correct?
myininaya
  • myininaya
48 pi is right!
anonymous
  • anonymous
Thanks!!

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