MCV4U: (Curve Sketching)

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8. A function is defined by f(x) = ax3 + bx + cx + d. Find the values of a, b, c, and d, if f(x) has a local minimum at (o. -8) and a point of inflection at (-1,-2). (9 marks)6. Given the function g(x) = -5x . ) State the domain. (1 mark) b) Determine the intervals of increase/decrease and classify any critical values. Determine the coordinates of any critical points. (4 marks) c) Determine the intervals of concavity and the coordinates of any points of inflection. (5 marks) Use your results from a) to c) to sketch a graph of the function, g(x). (1 mark)A box is to be constructed so that its base is two and a half times as long as it is wide. Its volume is to be 1800 em. The cardboard for the box costs 0.2c/cm?, but the cardboard for the bottom is thicker, so it costs twice times as much. Find the dimensions that will minimize the cost of the cardboard, to the nearest hundredth of a centimeter. This is NOT an open-top box. (7 marks) h W 2.5w