The graph of the second derivative of a function g is shown

The graph of the second derivative of a function g is shown below. Use this graph to answer the following questions about g and g\' Where is g up? Where does g have points of inflection? Rank the four numbers g\'(0), g\'(1),g\'(2) and g\'(3) in increasing order. Suppose that g\'(1) = -1 increasing or decreasing at x = 2? Justify your answer

Solution

a)concave up when second derivitive is pos so 0<=x<=3 b)points of inflection when second derivitive=0 and concavity changes so x=3 c)slope is increasing the whole time from 0 to 3 so g\'(3)>g\'(2)>g\'(1)>g\'(0) d)at x=1 g is decreasing and the slope does not increase by more than 1 before x=2 so g is still decreasing