Why Is There Only One Stationary Point for the Volume of This Box?

[Andy21]

Homework Statement

The volume of a box is given by V=4x^3 -66x^2 +216x. Explain why there is only one value of x for which V is stationary?

Homework Equations

The Attempt at a Solution

dV/dx = 12x^2 -132x +216 at a stationary point x^2-11x+18=0 so x=2 or 9

 

[vela]

You need to check if those solutions are reasonable since you're talking about a physical situation. What are the volumes for those two points?

 

[Andy21]

I got a volume of -486 for x=9 and 200 for x=2. I think that the one stationary point must be at x=2 because a box can't have a negative volume. Is this correct?

 

[HallsofIvy]

Yes, that's exactly it.

 

[Andy21]

Thanks for the help