The graph of g (x) = ax3 + bx2+ cx, a cubic function having a y-intercept of 0, is drawn below. The x-coordinates of the turning points of g are -1 and 2.
8.1 For which values of x will g increase? (2)
8.2 Write down the x-coordinate of the point of inflection of g. (2)
8.3 For which values of x will g be concave down? (2)
8.4 If g'(x) = – 6x2 + 6x + 12, determine the equation of g. (4)
8.5 Determine the equation of the tangent to g that has the maximum gradient. Write your answer in the form y = mx + c . (5)
[15]