13. An observer is watching the launching of a rocket at a location 100 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 e. 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/ dt,if the rocket is at a height of h = 100 ft and moving at a rate of dh/dt = 500 mph Also evaluate when the height is h = 500 and the speed is dh/dt = 750 mph QUESTION 14 derivative of inverse Consider the function f(x) given as follows f(x) = (x- 3)3 +5 { f(x) = (x-3)^3 + 5 } Find the inverse function [F-1](x) { [f^-1)] (x) } Sketch the graph of f(x) and its inverse [FM-1)] (x) and describe the relation between the graphs. Evalutate f(2) and sketch the tangent line to f(x) at x=2. Similarly evaluate [f^(-1)] ' (4) and sketch the tangent line to [f^(-1)] (x) at x=4. Explain the relation between the two tangent lines and their slopes QUESTION 15 derivative of inverse In this problem we apply the following formula to evaluate the derivatve of f-1 (x), the inverse of f(x). [F1])(b) = 1/f(a) where f(a) = b OR [f-l](b) = a Apply this formula to find [f-1 (2) where f(x) = x3 + 3 x2 - 2 a = 2 { [f^(-1)]' (2) } { f(x) = x^3 + 3x^2 - 2 } { a = 2 } QUESTION 16 Derivative of logarithm Find f(x), the derivative of f(x) given by f(x) = x In [x? sec x]