An observer is watching the launching of a rocket at a location 500 ft form the base of the rocket. The angle A. (th), for the observer represents the angle of elevation from the ground level to the height of the rocket. a) Write an equation relating the variable h, the height of the rocket to this angle of elevation 0. b) Take the derivative and apply the methods from related rates to find the rate of change of the angel of elevation, de /dt, in terms of the speed of the rocket dh/dt. c) Evaluate this rate of change de/ dtif the rocket is at a height of h = 250 ft and moving at a rate of dh/dt = 450 mph and when the height is h = 500 sgrt(3) ft -- 866.03 ft. and the speed is dh/dt = 450 mph Also evaluate when the height is h = 1500 and the speed is dh/dt = 700 mph QUESTION 14 Optimization on interval a,b) Find all critical points for each of the following functions. a) { f(x) = x^3 -2x^2 -4x + 5 b) { g(x) = [ ( sqrt(x-4) )/ (3x+1)] c) Optimize f(x) on the interval [-1, 5]