Determine the values of x that would maximize the volume

Question

Volume = x^3 - 7x^2 + 12x

Answer 1

Let V = x³ -7x²+12x dV/dx = 3x²-14x+12 Setting dV/dt = 0 we find that the two values of

x = 1.131 and 3.535

Substituting these values into the Volume formula we get

V = 6.065 if x = 1.131

V = -.879 if x = 3.535 However, these values are local maximum value canidates and the equation & problem contains no constraints. So any x value greater than x = 4.67 gives a volume greater than 6.065! Therefore, there is no distinct absolute maximum for this problem!