Find Derivative/maximum/inflection from a graph?

http://img4.imageshack.us/img4/9660/testfinal.jpg

**Let g be a continuous function with g(2)=5. The graph of the piecewise-linear function g ' the derivative of g, is shown above for -3<=x<=7.**

**a) Find the x coordinate of all points of inflection of the graph of y=g(x) for -3<x<7. Justify your answer.**

**b) Find the absolute maximum value of g on the interval -3<=x<=7. Justify your answer. **

**c)Find the average rate of change of g(x) on the interval -3<=x<=7.**

a. point of inflection is where x changes sign, so it would be at -1, 1, 4, right?

b. i know where the maximum is on the derivative graph, but the original I don't know

c) -1-4/7+3= -1/2 right?