A twice–differentiable function p on (−∞,∞) has these characteristics:
• p is concave up on (−∞,−2) and concave down on (−2,1).
• p is increasing on (−∞,0) and decreasing on (0,3).
• p has a point of inflection at x=−2 and a relative maximum at x=0.
Which statement about the first derivative p′ is most consistent with this information?
a) p′ has a local minimum at x=−2, with p′(x)>0 for −2<x<0, p′(0)=0, and p′(x)<0 for 0<x<3.
b) p′ has a local maximum at x=−2, satisfies p′(x)>0 for −2<x<0, equals 0 at x=0, and p′(x)<0 for 0<x<3.
c) p′ equals 0 at x=−2, remains positive on (−2,0), has p′(0)=0, and is negative on (0,3).
d) p′ has a local minimum at x=0, equals 0 at x=0, is negative for −2<x<0, and positive for 0<x<3.