the volume in cubic inches of a recrangular prosom can be modeled by the function f(x)= 12(x-3)(6-x). what is the maximum volume of the prism?

Answerfriction

Iam pretty sure it is c.

You're asking in the ap section, so i'll give the ap calculus-style answer. alternatively, you can find the vertex of the parabola and use the "y"-coordinate as the answer.

the maximum height can occur at a critical number, that is, a number  such that  .

the derivative of  can be calculated as follows:



find a value of  that is a zero of the derivative:


this is parabola that is opening downward; we can assume there is a maximum at  .

to find that maximum, calculate  .