Question

The volume of the cylinder if V(x)
. When we solve the equation V′(x)=0
what does the answer tell us?

Answer 1

When we solve the equation V'(x) = 0, we are finding the value of x at which the rate of change of the volume of the cylinder with respect to its dimensions is equal to zero. This means that at that specific value of x, the volume of the cylinder is either at a local maximum or minimum. In other words, the answer tells us the dimensions of the cylinder that result in the greatest or smallest volume for a given set of constraints.