Question

A closed box with a square base is to be made from 300 cm2 of a certain material. Find the dimensions of the box with maximum volume.

Answer 1

Let side of square be a
a^2 = 300
Find the max for x using 1st derivative test

Answer 2

could you be a little more specific in the procedure, please? thank you!

Answer 3

Let x = length of side of base and y = height of box.

Surface area
\[A=2x^2+4xy\\
300=2x^2+4xy\]
Volume
\[V=x^2y\]
Find an expression for y in terms of x using the surface area equation:
\[300=2x^2+4xy\\
\Rightarrow y=\frac{300-2x^2}{4x}\]
Substitute this into the volume equation, then apply the first derivative test.

Answer 4

thank you so much!!