#8: Please Answer Questions 52 - 56. Thank you.

52. Find an equation of the line through the point (3, 5) that cuts off the least area from the rst quadrant. 53. Let a and b be positive numbers. Find the length of the short est line segment that is cut off by the rst quadrant and passes through the point (a, b). 54. At which points on the curve y = l + 40x3 3x5 does the F tangent line'have the largest slope? 55. What is the shortest possible length of the line segment that is cut off by the rst quadrant and is tangent to the curve y = 3/x at some point? 56. What is the smallest possible area of the triangle that is cut off by the rst quadrant and Whose hypotenuse is tangent to the parabola y = 4 - x2 at some point? CAE