I need questions 44-54 only even ones done with all work shown.

Section 3.7 Implicit Differentiation 163 43. Which of the following could be true if f"(x) = 1/37 ( @) f ( x ) = 2123 - 3 47. (a) Confirm that (-1, 1) is on the curve defined by (b) f (x) = 20513 -7 x y2 = cos (Try). (@)f" ( x ) = - 2x-4/3 ( d) f' ( x ) = 2x23 +6 (b) Use part (a) to find the slope of the line tangent to the curve at (-1, 1). 44. Which of the following could be true if g"(1) = 1/3/4? 48. Grouping Activity (a) 8' (1 ) = 4V/1 -4 (b) g" ( 1 ) = -4/Vi (a) Show that the relation (c) 8 (1) = 1 - 7+ ( 16/5) 15/4 (d) 8' (1 ) = (1/4)1 1/4 ys - xy = -1 45. The Eight Curve (a) Find the slopes of the figure-eight- cannot be a function of x by showing that there is more than one shaped curve . possible y-value when x = 2. 1 4 = 12 - x 2 (b) On a small enough square with center (2, 1), the part at the two points shown on the graph that follows. of the graph of the relation within the square will define a (b) Use parametric mode and the two pairs of parametric function y = f(x). For this function, find f'(2) and f"(2). equations 49. Find the two points where the curve x2 + xy + y? = 7 crosses * , (1 ) = V12 - 14 , vi(1 ) = 1 , the x-axis, and show that the tangents to the curve at these *2 (1 ) = - V12 - 14 , y2 (1 ) = 1, points are parallel. What is the common slope of these tangents? 50. Find points on the curve x2 + xy + y2 = 7 (a) where the tangent to graph the curve. Specify a window and a parameter interval. is parallel to the x-axis and (b) where the tangent is parallel to the y-axis. (In the latter case, dy/dx is not defined, but dx/dy is. What value does dx/dy have at these points?) 51. Orthogonal Curves Two curves are orthogonal at a point of intersection if their tangents at that point cross at right angles. Show that the curves 2x2 + 3y2 = 5 and y? = x3 are orthogonal at (1, 1) and (1, -1). Use parametric mode to draw the curves and to show the tangent lines. 52. The position of a body moving along a coordinate line at time t is s = (4 + 6t)3/2, with s in meters and t in seconds. Find the body's velocity and acceleration when t = 2 sec. 53. The velocity of a falling body is v = 8Vs - 1 + 1 feet per second at the instant t (sec) the body has fallen s feet from its starting point. Show that the body's acceleration is 32 ft/sec2. 54. The Devil's Curve (Gabriel Cramer [the Cramer of Cramer's Rule], 1750) Find the slopes of the devil's curve y4 - 4y2 = x4 - 9x2 at the four indicated points. 46. The Cissoid of Diocles (dates from about 200 B.C.) y4 - 4y2 =14- 9x2 (a) Find equations for the tangent and normal to the cissoid of Diocles, 12 ( 2 - x ) = x3, at the point (1, 1) as pictured below. (-3, 2) 1 (3, 2) (b) Explain how to reproduce the graph on a grapher. and the 1 2(2 - x ) = x3 (-3, -2) (3, -2 (1, 1) 55. The Folium of Descartes (See Figure 3.47 on page 157) (a) Find the slope of the folium of Descartes, x3 + y3 - 9xy at the points (4, 2) and (2, 4). (b) At what point other than the origin does the folium have horizontal tangent? (c) Find the coordinates of the point A in Figure 3.47, wher folium has a vertical tangent