Find the Maximum

[raven720]

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

 

[BigGlenntheHeavy]

\(\displaystyle S \ = \ kh^{2}w \ and \ h^{2}+w^{2} \ = \ (60)^{2}\)

\(\displaystyle Can \ you \ take \ it \ from \ here?\)

 

[raven720]

so then S' = 2khw + kh^2

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

 

[BigGlenntheHeavy]

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

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

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

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