The figure above shows the graph of f ', the derivative of a twice-differentiable function f, on the interval [–3, 4]. Answer the following questions based on the graph of f '. a) Find all x-coordinates at which f has a relative minimum. Justify your answer.
b) On what open intervals contained in [–3, 4] is the graph of f both concave up and decreasing? Justify your answer.
c) Find the x-coordinates of all points of inflection on the graph of f.
d) What is the average rate of change of f ' between x = 0 and x = 3?