Question 1170207: the alloysean aluminum company has hired you to design a cylindrical can.you are given expressions for both the radius :(5-x) centimeters and the height:(2x+1) centimeters.
creat a function in polynomial form for the volume of the cylinder .( v r^2 h)
graph the polynomial function
describe the nearest tenth , the intervals on which the polynomial function is increasing and the intervals on which it is decreasing , NEED ASAP . less than 10 min
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! volume is π*r^2*h
=(5-x)^2*(2x+1)*π
The domain is [0,5), so while the function is graphed outside that here, it is only valid within the domain.
derivative ix (5-x)^2*(2)+(2x+1)*2(5-x)(-1)
=this is 6x^2-38x+40
That equals 0 when x=1.33 and when x=5
 graph of derivative
So the polynomial is increasing on the interval [0, 4/3)] and decreasing on the interval ((4/3), 5)
Note: if you use 1.3, to the nearest tenth, then there is a closed interval for the first [0, 1.3], because 1.3 is in the interval. But the second would not be [1.3 and 5) because it is not decreasing on the interval 1.30 to 1.33. I suspect this will not be an issue in the answer, but it is worth considering. There are more issues with intervals even when there isn't rounding, but they are omitted here.
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