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a.)At what point does the curve x∧3−9x∧ 2−y=0 have a slope of 10 ? b.) What is the equation of the line, tangent to the curve f(x)=2x−x∧2 * at (2,0) ? a. 2x−y=4 c. y−2x=4 b. 2x+y=4 d. 2x+y=−4 c.) Find the radius of the curvature of the parabola y2−8x=0 at point (4,4sqrt(2))  a. 20.79​ c. 29.07​ b. 27.90 d. 27.09 d.) A rectangular plot of land is to be surrounded by a fence and then divided into 2 equal parts by a fence parallel to one side. The area bounded is 1875 sq. ft. What are the dimensions of the rectangle that require the least amount of fence? a. 125∧ prime * 15∧ prime b. 75∧ prime * 25∧ prime c. 93.75∧ prime ∗20∧ prime d. 62.5∧ prime * 30∧ prime e.) An open box is made from a rectangular piece of tin 5′′ by 8 " by cutting out equal squares at each corner and then folding up the remaining flaps. What square sizes should be cut out so that the box will have a maximum volume? d.) Find the minimum amount of tin sheet that can be made into an open cylinder having a volume of 12 cubic centimeters in square centimeters. a. 106.90c∗ m∧2 b. 126.90c∗ m∧2 c. 116.90c∗m∧2 d. 136.90 cm2 e.) A closed rectangular box with square base is to have a capacity of 16823cu. in. Find the height of the box that requires minimum amount of material required. a. 25.6322in. b. 26.5232in. c. 25.6232 in. d. 26.5322in.