Question

6. On the axis below, sketch the graph of a continuous function y = f(:) having all of the following properties. Points are awarded for accuracy and neatness. [12 points) (i) f(0) = 3 and f(3) = 0 (ii) f'(-2) = f '(1) = 0 (iii) f is not differentiable at r=-1 (iv) [(x) > 0 for all & € (-0,3) (v) lim f(x) = 0 and lim,- S(:) = -1 (vi) F"(x) > 0 for all x € (-20, -3) and f "(c) < 0 for all 2 € (-1,2) (vii) (-3,2) is a point of inflection of f