3. (a) Find the slope of the tangent line to the parabola v = x' + 3x at the point (-1, -2) (i) using Definition 1 (ii) using Equation 2 (b) Find an equation of the tangent line in part (a). (c) Graph the parabola and the tangent line. As a check on your work, zoom in toward the point (-1, -2) until the parabola and the tangent line are indistinguishable.5-8 Find an equation of the tangent line to the curve at the given point. 5. y = 2x- - 5x + 1. (3,4)\f11. A cliff diver plunges from a height of 100 ft above the water surface. The distance the diver falls in t seconds is given by the function d(t) = 16t- ft. (a) After how many seconds will the diver hit the water? (b) With what velocity does the diver hit the water?15. (a) A particle starts by moving to the right along a horizon- tal line; the graph of its position function is shown in the figure. When is the particle moving to the right? Moving to the left? Standing still? (b) Draw a graph of the velocity function. s (meters) 4 4 2 2 4 6 / (seconds)17. For the function g whose graph is given, arrange the follow- ing numbers in increasing order and explain your reasoning: 0 g'(-2) g'(0) g'(2 ) g'(4) y = g(x) -10 2 3 439. Sketch the graph of a function f for which f(0) = 0, f'(0) = 3, f'(1) = 0, and f'(2) = -1.41. Sketch the graph of a function g that is continuous on its domain (-5, 5) and where g(0) = 1, g'(0) = 1, g'(-2) = 0, lim,-_s+ g(x) = 0, and lim, -s- g(x) = 3