Luke53 wrote:Hi, can someone help me getting started with this problem?

The stiffness of a rectangular beam varies as its breadth and as the cube of its hight. Find the dimensions of the stiffest beam which can be cut from a circular log 12 inches in diameter.

to get started try

here.

For this one, I think you have to use the pythagorean thm to relate the diameter to the breadth (b) & height (h). The diameter is d = sqrt{b^2 + h^2} so d^2 = b^2 + h^2 = 12^2 = 144. Solve this for b to get b = sqrt{144 - h^2} If stiffness is S then S = bh^3 = sqrt{144 - h^2}*h^3. Do the derivative to find the max/min.