A twice-differentiable function f satisfies f′(1)=0 and f′(4)=0. Additional information is f′′(1)=−3 and f′′(4)=5. Which of the following statements about f is true?
a) f has a local minimum at x=1 and a local maximum at x=4.
b) f has inflection points at both x=1 and x=4.
c) f has a local maximum at x=1 and a local minimum at x=4.
d) f has a local maximum at x=1 and an inflection point at x=4.