Find the Maximum

raven720

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Nov 24, 2009
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A rectangular beam is cut from a cylindrical log of radius 30cm. The strength of the beam is jointly proportional to the width w and the square of the height h. Find the width and height of the beam of max strength.

Mainly i just need help finding the equation and the derivitive from there im sure i can get it
 
S = kh2w and h2+w2 = (60)2\displaystyle S \ = \ kh^{2}w \ and \ h^{2}+w^{2} \ = \ (60)^{2}

Can you take it from here?\displaystyle Can \ you \ take \ it \ from \ here?
 
so then S' = 2khw + kh^2

where does the w^2 + h^2 = (60)^2 come from?
and from that w = 60 - h?
 
where does the w^2 + h^2 = (60)^2 come from?
and from that w = 60 - h?

Sorry, raven720, I wont help you any further. If you cant figure it out, you are over your\displaystyle Sorry, \ raven720, \ I \ won't \ help \ you \ any \ further. \ If \ you \ can't \ figure \ it \ out, \ you \ are \ over \ your

 head. Perhaps basket weaving is more of your forte.\displaystyle \ head. \ Perhaps \ basket \ weaving \ is \ more \ of \ your \ forte.

Hint: Read the problem.\displaystyle Hint: \ Read \ the \ problem.
 
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