help - derivatives?

Question

Answer 1

Step 1:

The dimensions of the open-topped box are .

Formula for the volume is .

The volume of the box is .

Apply derivative on each side with respect to .

.

Step 2:

Maximum volume is obtained when

Find the critical numbers by equating .

Solve the above equation using quadratic formula.

and

and .

Comments

Step 3:

Find the maximum volume by substituting values of in .

When ,

cubic inches.

Volume can't be negative, it is not considered.

When ,

cubic inches.

Therefore, the height of the box is 1.48 inches.

Solution:

The height of the box is 1.48 inches.