Review function and derivative graphs by matching slopes, extrema, concavity and zero crossings across related plots, then explaining the correspondence.
The graph of the continuous function g, the derivative of the function f, is shown above. The function g is piecewise linear for −5≤x<3, and g(x)=2(x−4)2 for 3≤x≤6.
For -5<x<6, on what open intervals, if any, is the graph of f both increasing and concave up? Give a reason for your answer.
The graph of f is increasing and concave up on 0<x<1 and 4<x<6 because f′(x)=g(x)>0 and f′(x)=g(x) is increasing on those intervals.