1. Graph Sketching. If possible, sketch a graph of y : f (cc) such that: a f(:l?) has domain (414), - f'($) > 0 on (2, 2) and f'($) 0 everywhere it is dened Note: Be sure to pay attention to when you are reading about f , f\" or f\". 2. Graph Sketching. If possible, sketch a graph of y = f(x) such that: lim f'(x) = 0 and f'(x) > 0 on (-00, 0) lim f (a) = 00 and lim f'(x) = NIH Note: Be sure to pay attention to when you are reading about f, f' or f". 2.a. Assuming f"(x) is defined on (-oo, 0), what is the sign of f"(x) on (-co, 0)? 2.b. Assuming f"(x) is defined on (0, co), what is the sign of f"(x) on (0, co)?3. Modeling: Finding the Best Angle. Consider a soccer player dribbling along a. line perpendicular to the end line and is 6 yards away from the nearest goal post. Let 37 represent the distance (in yards) the player is away from the end line, and let I9 represent the angle centered at the player and formed by the lines between the player and the goal posts. Note: The width of a standard soccer goal is 8 yards. 6 yds 8 yds Write 9 in terms of 3:. Determine the value of a: that maximizes the player's shot on goal (i.e., that maximizes the value of 9)