Hi, I'm having a hard time with this question.
the stiffness of a beam is proportional to it's width times the cube of it's depth. What are the dimensions of the stiffest beam you an produce from a beam 12" in diameter.
So I draw a rectangle inside a circle, and the diagonal inside the rectangle is 12. The width (w) times the depth cubed equals the stiffness.
boils down to -d^2(6d^2+d-864)=0, to find critical points.
d=0, or 6d^2+d-864=0
did I do this right?
The teacher, tried to get us started on this problem, but following through from where he started, I run into a problem which I don't understand.
The teacher, started by trying to find ds/dw.
Here is where he left us off, S=W(144-w^2)^(3/2)
I found it's derivative, 3w^2sqr(144-w^2)+(144-w^2)^3/2
when I solve for 0, I get w=-12, or 12.
Makes no sense because if the width is 12, the depth is zero. Where did I go wrong.