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anonymous
 one year ago
The surface area of a right circular cylinder of height 5 feet and radius r feet is given by S(r)=2πrh+2πr2. Find the instantaneous rate of change of the surface area with respect to the radius, r, when r = 6.
anonymous
 one year ago
The surface area of a right circular cylinder of height 5 feet and radius r feet is given by S(r)=2πrh+2πr2. Find the instantaneous rate of change of the surface area with respect to the radius, r, when r = 6.

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zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1\[\Large\rm S(r)=2\pi r h+2\pi r^2\]Hey Camila! :) Have you learned your derivative shortcuts at this point? Or do we have to use the limit definition for the derivative to find our instantaneous rate of change? _

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I know how to derive.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1We're holding the height, h, constant at 5.\[\Large\rm S(r)=2\pi r \cdot 5+2\pi r^2\]Simplifies our function a little bit, which is nice.\[\Large\rm S(r)=10\pi r+2\pi r^2\]

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1So apply your power rule to each term, should be pretty straight forward :) Are you getting confused because of all that pi nonsense mixed in?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yeah that was the part that confused me.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1\[\Large\rm (10\pi x)'=10\pi(x)'=10\pi (1)\]Normal power rule, ignoring the constant coefficients :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So I would get 10π+4πr and plug in 6 for r?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1\[\Large\rm S'(r)=10 \pi+4\pi r\]Good good good.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So when I plug that in it would be 34π right?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Yayyy good job! *\c:/* Camila <*c:/*

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Haha okay thank you so much!
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