zeesbrat3
  • zeesbrat3
The surface area, S, of a sphere of radius r feet is S = S(r) = 4πr2. Find the instantaneous rate of change of the surface area with respect to the radius r at r = 8.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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zeesbrat3
  • zeesbrat3
So do you find r'? Which would end up as 64π?
ganeshie8
  • ganeshie8
Careful, you're finding S'(r) here and yes it ends up being 64pi
Plasmataco
  • Plasmataco
yes, I think so

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zeesbrat3
  • zeesbrat3
You mean I might be learning something?! Finally!! Thank you everyone
anonymous
  • anonymous
the instantaneous rate of change of the surface area\[ \frac{dS}{dr} \]
anonymous
  • anonymous
\[ \frac{dS}{dr} = \frac{d\left(4\pi r^2\right)}{dr} \]
zeesbrat3
  • zeesbrat3
Then the product rule if I remember the name correctly.. Right?
anonymous
  • anonymous
You can use the product rule, but the power rule is intersting.
zeesbrat3
  • zeesbrat3
Sorry, I meant the power rule. Where you multiply the value of the exponent by the coefficient and then decrease the exponent by 1
anonymous
  • anonymous
See what happens
zeesbrat3
  • zeesbrat3
8πr 8π(8) 64π
anonymous
  • anonymous
Remember units
zeesbrat3
  • zeesbrat3
ft^3 right?
anonymous
  • anonymous
Nope
anonymous
  • anonymous
When you substituted in \(r=8\), you should have put in the \(\text {ft}\) as well.

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