6. A fuel truck, has a cylindrical tank of radius R = 2 m and length L = 10 m lying horizontally. The volume of gasoline in the tank is given by V = L (R2 cos'1 (Rik) (R h)\\/2Rhh2) where h is the vertical height of the gasoline in the tank. If gasoline is being pumped into the tank at a rate of 2 m3/min, how fast is the gasoline level rising when the height h of the gasoline is 1 m? 7. Consider the function f($) = 692/2 + 334/12 + 932/2 3:12 (a) Use the Intermediate Value Theorem to show that f has at least one critical point. (b) Use Rolle's Theorem to show that this is the only critical point. (c) Use The Extreme Value Theorem to show that the critical point is an (absolute) min imum of f on some bounded interval [(1, b]. (No marks will be assigned for using other methods). 8. An object weighting to pounds on the surface of the earth, will weight sz at distance a: from the center of the earth, where R = 3, 960 miles is the radius of the earth. Use linear approximation to estimate the weight lost by a 160 lb passenger ying in an airplane at an altitude h of 6 miles