Thread: Find Derivative/maximum/inflection from a graph?

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?

you are given a graph of g'(x) , the derivative of g(x).

g(x) has extrema where g'(x) changes sign

g(x) has inflection points where the slope of g'(x), which is g''(x), changes sign.