FIND THE VOLUME OF THE BOX IN TERM OF X ONLY

An open rectagular -based box has a lenght of 2x cm, width x cm and height (300-x^2)/3x
FIND THE VOLUME OF THE BOX IN TERM OF X ONLY AND USED CALCULUS TO FIND THE VALUE OF X SO THAT THE VOLUME OF THE BOX IS A MAXIMUM

V = 2x(x)(300 - x^2)/(3x) = 2x(300 - x^2)/3 = (600x - 2x^3)/3 = 200x - 2/3 x^3

dV/dx = 200 - 2x^2 = 0
200 = 2x^2
100 = x^2
x = 10

v = lwh
v = (2x)(x)(300-x^2/3x) - (2x/3)(300-x^2) = (600x - 2x^3/3) = 200x - 2x^3/3