29- 32. 1 2 3 4 x 44. Find the tangent line to the Witch of Agnesi (graphed here) at the ercises point (2, 1). = x2 + 4 2 45. Quadratic tangent to identity function The curve y = O ax2 + bx + c passes through the point (1, 2) and is tangent to the line y = x at the origin. Find a, b, and c. 46. Quadratics having a common tangent The curves x2 + ax + band y = ex - x2 have a common tangent line point (1, 0). Find a, b, and c. 47. Find all points (x, y) on the graph of f(x) = 3x2 - 4x with t. gent lines parallel to the line y = 8x + 5. 48. Find all points (x, y) on the graph of g(x) = 2x3 - 3x2 + 1 with tangent lines parallel to the line 8x - 2y = 1. 49. Find all points (x, y) on the graph of y = x/(x - 2) with tangent lines perpendicular to the line y = 2x + 3. 50. Find all points (x, y) on the graph of f(x) = x2 with tangent lines passing through the point (3, 8). f(x) = x2 10 (3, 8) (x, y) -2 51. Assume that functions f and g are differentiable with f(1) = 2, - f'(1) = -3, 8(1) = 4, and g'(1) = -2. Find the equation of the line tangent to the graph of F(x) = f(x)g(x) at x = 1. 52. Assume that functions f and g are differentiable with f(2) = 3, f'(2) = -1, 8(2) = -4, and g'(2) = 1. Find an equation of the f(x) + 3 line perpendicular to the graph of F(x) = x - g(x) at x = 2