Maxima and Minima in Calculus

A rectangular garden is to be fenced with 100 meters of fencing. What dimensions will maximize the area of the garden?

• 25 meters by 25 meters

• 20 meters by 30 meters

• 10 meters by 40 meters

• 15 meters by 35 meters

In an electrical circuit, the power P (in watts) is given by the formula P = IV, where I is the current in amperes and V is the voltage in volts. If the current is fixed at 5A, what voltage will maximize the power output?

• The voltage should be 10V.

• The voltage should be 0V.

• The voltage should be 2.5V.

• The voltage should be as high as possible.

Find the maximum volume of a box with a square base and an open top, given that the surface area is 600 square meters.

• 900 cubic meters

• 1500 cubic meters

• 1200 cubic meters

• 1800 cubic meters

A company wants to design a cylindrical can that will hold 1 liter of liquid. What dimensions will minimize the amount of material used for the can?

• Radius: 6.00 cm, Height: 10.00 cm

• Radius: 4.00 cm, Height: 15.00 cm

• Radius: 5.42 cm, Height: 11.84 cm

• Radius: 5.00 cm, Height: 12.00 cm

Determine the dimensions of a rectangular box with a square base that has a volume of 500 cubic centimeters and minimizes the surface area.

• Base: 10 cm x 10 cm, Height: 5 cm

• Base: 5 cm x 5 cm, Height: 20 cm

• Base: 12 cm x 12 cm, Height: 3.47 cm

• Base: 8 cm x 8 cm, Height: 7.5 cm