A twice–differentiable function f satisfies the following conditions:
• f′(x)=0 at x=−4,−1,2 and nowhere else.
• f′(x)>0 on (−4,−1) and (2,∞).
• f′(x)<0 on (−∞,−4) and (−1,2).
• f′′(x)<0 on (−4,0) and f′′(x)>0 on (0,∞).
Which statement is most consistent with these conditions?
a) f has local maxima at x=−4 and x=2, a local minimum at x=−1, and a point of inflection at x=0.
b) f has local minima at x=−4 and x=2, a local maximum at x=−1, and a point of inflection at x=0.
c) f has local minima at x=−4 and x=2, a local maximum at x=−1, and no points of inflection.
d) f has local minima at x=−4 and x=−1, a local maximum at x=2, and a point of inflection at x=−1.