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Math Help - Find Derivative/maximum/inflection from a graph?

  1. #1
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    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?
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  2. #2
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    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.
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