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ap calculus help please?!?
you are planning on making an open rectangular box from an 8- by 15-in piece of cardboard by cutting congruent squares from the corners and folding up the sides. what are the dimensions of the box of largest volume you can make this way and what is its volume
1 Answer
- ?Lv 68 years agoFavorite Answer
V(x) = (15 - 2x)(8 - 2x)x
V(x) = 4x^3 - 46x^2 + 120x
Then, we take the derivative.
V '(x) = 12x^2 - 92x + 120
We set it equal to zero and solve for x
12x^2 - 92x + 120 = 0
A' = 0 at x = 5/3
length = 15 - 10/3 = 25/3 in
width = 8 - 10/3 = 14/3 in
h = 5/3 in
V = 64.81 in^3