Question

HELP ASAP DESPERATE_ CALCULUS

Answer 1

Let each side of the square thats cut out be x inches
so the box will have dimensions:-
height = x , length = 20-2x and width = 10-2x
the volume of the box is
V = x(10-2x)(20-2x) = x(200 - 60x + 4x^2) = 4x^3 - 60x^2 + 200x
we need to find the value of x for which this V is a maximum
Find the derivative:-

dV/dt = 12x^2 - 120x + 200
this equals zero for max/min value
12x^2 - 120x + 200 = 0

solving for x gives x = 7.887 and x = 2.113

which value gives a maximum volume? We need to look at the second derivative:-

d^2 y / dx^2 = 24x - 120 which is positive for x= 7.887 and negative for x = 2.113
so x = 2.113 gives a maxm. This maximum value of V is 2.113(10 - 2*2.113)(20-2*2.113))
This maximum value of the volume = 192.5 cubic inches

Answer 2

is that all @celticcat thad you by the way- now i can study t

Answer 3

Huh? I think that is a lot of information, man lol