The design of a digital box camera maximizes the volume while keeping the sum of the dimensions at 6 inches. if the length must be 1.5 time the height, what should each dimension be?

which simplifies to 

and so we take the derivative of that function in terms of l

then we set that to 0

using the quadratic formula


simplifying..




at this point i noticed an error, i used l instead of h... but thats ok

pluggin 0 and 1.6 for h, lets check answers
1.6: h=1.6 l=2.4 w=2
0: h=0 l=0 w=6

so the answer is h=1.6 l=2.4 w=2, which gives the greatest volume of 7.68