Difficult Optimisation problem (maximizing a cuboid)

[don1231915]

Difficult Optimisation problem! (maximizing a cuboid)

Find derivate d(x)

 

[JeSuisConf]

Well, just cut in in half on the y-axis. The base of half your cuboid (... a rectangle or square in this case...) is just x. The height is 1296-x^2. We're looking on x=0 to 36, right? Well, almost. At what value of x is the height going to be at least 75% of the base? Then what's the area of this half rectangle? Can you find the optimum using calculus?

 

[JeSuisConf]

Ok, it made it easier for me to think about but forget about what i said about cutting it in half.

If x were greater than 36, then you would be outside the ellipse, but you want to say inside.

Think of creating your rectangle using the variable x. If I set one corner at (x,0), then I can set another corner at (x, sqrt(1296-x^2)). So it has width 2x and height sqrt(1296-x^2). Therefore the area is ____ ?

Regarding the 75% thing - for what x will the height be exactly 75% of the width? Now for what values is it less than 75% of the width? Think that you want sqrt(1296-x^2) to be less than 75% of 2x.