A box without a top is to be made from a rectangular piece of cardboard, with dimensions 4 in. by 8 in., by cutting out square c
orners with side length x and folding up the sides.
Write an equation for the volume V of the box in terms of x.
Use technology to estimate the value of x, to the nearest tenth, that gives the greatest volume. Explain your process.
Write an equation for the volume V of the box in terms of x.
Use technology to estimate the value of x, to the nearest tenth, that gives the greatest volume. Explain your process.
1 answer:
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If
then the derivative is
Critical points occur where . This happens for
In the first case, we find
In the second,
So all the critical points occur at multiples of , or
. (This includes all the even multiples of
.)
For this case we have:
By trigonometric property we have:
Where:
Substituting:
Clearing x we have:
Thus, the equation is:
Answer: