Prism Volume Lab
Hey there. Just had a couple of quick pre-calc lab questions, so here goes:
Recall that the volume of a prism is V = l x w x h. Using function notation, volume can be represented in terms of x as V(x) = L(x) x W(x) x H(x). The rectangular prism is represented by V(x) = -x^3 - 2x^2 + 16x + 3, where x is in inches.
- I've found that x = plus or minus 4 and -2.
- I know that the maximum volume is 48.5, where the x value is 1.7.
I need help with the following:
- To the nearest tenth, what are the dimensions of the rectangular prism when its volume is at its maxium? Show your work, please.
- Using interval notation, state the possible values of x that will create a rectangular prism whose volume is represented as V(x) = -x^3 - 2x^2 + 16x + 32. Again, show your work please.
If anybody could help me out with these two questions, I would greatly appreciate it.