Expand your horizons with the diverse and informative answers found on IDNLearn.com. Our platform provides prompt, accurate answers from experts ready to assist you with any question you may have.

Find the value of x that maximized the volume of the following:

X
5 - 2x
8 - 2x


O x= 5
O x= 10/3
O x= 1
O x= 2.5


Find The Value Of X That Maximized The Volume Of The Following X 5 2x 8 2x O X 5 O X 103 O X 1 O X 25 class=

Sagot :

Check the picture below.

as you can see, the graph of the volume function comes from below goes up up up, reaches a U-turn then goes down down, U-turns again then back up to infinity.

the maximum is reached at the close up you see in the picture on the right-side.

Why we don't use a higher value from the graph since it's going to infinity?

well, "x" is constrained by the lengths of the box, specifically by the length of the smaller side, namely 5 - 2x, so whatever "x" is, it can't never zero out the smaller side, and that'd happen when x = 2.5, how so? well 5 - 2(2.5) = 0, so "x" whatever value is may be, must be less than 2.5, but more than 0, and within those constraints the maximum you see in the picture is obtained.

View image Jdoe0001