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October 6th, 2014, 07:54 AM  #1  
Senior Member Joined: Nov 2010 From: Indonesia Posts: 2,001 Thanks: 132 Math Focus: Trigonometry  Example in a Textbook, Which Got Me Confused Quote:
Maybe I would just stop here because here's where I got lost. How come the denominator $\displaystyle r^2$ didn't get derived? Could we just take h as a constant and didn't take it into account when deriving in respect to r despite it has r within it? Shouldn't the derivative be $\displaystyle S'(r)=2\pi r16,000\pi$ instead? Please give me some light on this. Last edited by skipjack; October 7th, 2014 at 06:47 PM.  
October 6th, 2014, 07:58 AM  #2  
Math Team Joined: May 2013 From: The Astral plane Posts: 2,043 Thanks: 818 Math Focus: Wibbly wobbly timeywimey stuff.  Quote:
Dan Last edited by skipjack; October 7th, 2014 at 06:46 PM.  
October 7th, 2014, 02:30 AM  #3 
Senior Member Joined: Apr 2014 From: Glasgow Posts: 2,139 Thanks: 721 Math Focus: Physics, mathematical modelling, numerical and computational solutions 
Be careful with the sign; the derivative of $\displaystyle \frac{1}{r}$ with respect to $\displaystyle r$ is $\displaystyle \frac{1}{r^2}$. Otherwise your calculation is fine.

October 7th, 2014, 06:31 PM  #4  
Global Moderator Joined: Dec 2006 Posts: 20,310 Thanks: 1981  Quote:
$\displaystyle S(r)=\pi r^2+2\pi rh=\pi r^2+2\pi r(\frac{8,000}{r^2})=\pi r^2+\frac{16,000\pi}{r}$ (Obtaining S as a function of r is useful, as h is a function of r.) You can proceed by use of differentiation or as shown below. $\displaystyle S = \pi((r^3  1200r + 16,000)/r + 1,200) = \pi((r20)^2(r + 40)/r + 1,200)$, which is minimized (for $r$ > 0) when $r$ = 20. The corresponding value of $h$ is also 20. Hence the required radius is 20cm and the required height is 20cm.  
October 8th, 2014, 12:01 AM  #5  
Senior Member Joined: Nov 2010 From: Indonesia Posts: 2,001 Thanks: 132 Math Focus: Trigonometry  Quote:
 

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