I'd really appreciate if I can see the answers with full steps

Assignment 3 Complete this assignment after you have finished Unit 4, and submit your work to your tutor for grading. Total points: 60 Weight: 10% (8 points) 1. Sketch the graph of the function f and its derivative function f' where if x5 -2 f (x) = if - 2 5 x 5 3 2 if x > 3 (16 points) 2. In each of the cases below, give the indicated derivative. You may not need to simplify your answers. d a. -x cos Vx - 3 dx b. 2 x tan x x-x d sin x - cos x C. dx d. If f(0) = 1, f'(0) = 2, g(0) = 0 and g'(0) = -1, find d f (x) - xg(x) dx f (x) + 8(x) =0 (8 points) 3. A softball diamond is a square whose sides are 18 m long. Suppose that a player running from first to second base has a speed of 7.5 m/s at the instant she is 3 m from second base. At what rate is the player's distance from home plate changing at that instant? Hint. Draw a diagram and locate the variables that change with respect to time. (5 points) 4. Let f(x) = x - a. Find the equation of the tangent line of the function f at the point (4, f(4)). b. Use differentials to estimate the value of f (4.02). (6 points) 5. Use implicit differentiation to prove that the curve x +y = (2x + 2yz -x)(see exercise 27 of page 187 of the textbook) has a vertical tangent line at the point (1,0)