A twice–differentiable function satisfies the following conditions: • at and nowhere else
MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
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.