The twice–differentiable function g is defined for −6≤x≤8. Its second derivative g′′ is piecewise constant and takes the following values.
• g′′(x)=3 for −6<x<−1
• g′′(x)=0 at x=−1
• g′′(x)=−2 for −1<x<4
• g′′(x)=0 at x=4
• g′′(x)=5 for 4<x≤8
Answer the following questions about the graph of g.
(a) Determine the interval(s) on which the graph of g is concave up and the interval(s) on which it is concave down on the domain −6<x<8. Express each interval using inequality notation.
(b) For each point x=−1 and x=4, state whether the graph of g has an inflection point there. Justify your conclusion by referring to the behavior of g′′ immediately to the left and right of each point.