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1. a) Use the rst principles (use limits) denition to differentiate y = 3x2 4x b) Differentiate the following using the correct derivative rules. Simplify the answers using positive exponents. i) y = J:3 sin(e') 2. Analyse the function using the algorithm for curve sketching under the foilowing headings. (a) Asymptote analysis (b) Concavity analysis f(x) = xix + 3F Only calculus techniques will be graded. No graphing calculator solutions will be considered. 3. A rectangular prism is constructed by using 12 wires thus creating a hollow solid. If the base of the prism is a square. determine the maximum volume of the prism if the total amount of wire used is 24 cm. Show all your work. Your solution must be calculus based. Any other solution will result in a mark of zero. 4. Given the regular hexagon, that is, all sides are equal and all angles are equal. Express QM in terms of x and y. Note: x and y are vectors. T is the centre of the hexagon. Note: vector OT = 3x - y and ON = 5x + y 5. Find the distance from the point (3.0.1) to the plane determined by the points A(4,2,1). B(6,0.5) and C(3,1.2). 6. Explain how the triple scalar product applies Wag planes in R3? Provide an example