Problem 24, Page 200

What does "largest" mean?? ... assume volume

Maximize volume:

substituting:

Taking the 1st derivative of the volume (with respect to L), setting it = zero, and solving for L yields:

Use L = 36 since L = 108 is nonsensical.

or using root finding function with a guess of:

L = 36, x = 18

Problem 26, Page 200

(Part A)

Given:

or

Maximize Volume:

Setting the drivative = zero and solving to find the maximum:

x = 12, y = 6

Problem 26, Page 200

(Part B)

Maximize volume

Given:

or

Maximize Volume:

x = 12, y = 6

Same dimensions as Part A... see below.

Problem 20, Page 191

finding the critical points by solving for the roots of the 1st derivative yields:

Maximum

Minimums

Problem 14, Page 221

Find:

(see example 3 on page 219)

so ...

Just for kicks, let's graph the function: