Prove each identity.

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10.

Prove each identity.

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10.

1. Find the exact global minimum value of on the domain

2. Find the exact global minimum and maximum values of on the domain

3. A certain quantity of gas occupies a volume of 20cc at a pressure of 1 atmosphere. The gas expands without the addition of heat, so, for some constant , its pressure, , and volume, , satisfy the equation . (a) Find the rate of change of pressure with respect to volume. (b) The volume is increasing at 2cc/min when the volume is 30cc. At that moment, is the pressure increasing or decreasing? How fast?

4. (a) A hemispherical bowl of radius 10cm contains water to a depth of cm. Find the radius of the surface of the water as a function of . (b) The water level drops at a rate of 0.1 cm per hour. At the what rate is the radius of the water decreasing when the depth is 5 cm?