For a twice-differentiable function f, the second derivative satisfies
f′′(x)>0 for −5<x<−1 and for x>3,
f′′(x)<0 for −1<x<3, and
f′′(x)=0 only at x=−1 and x=3.
Which statement is true about the concavity of f and its points of inflection on the interval (−5,6)?
a) f is concave down on (−5,−1)∪(3,6) and has points of inflection at x=−1 and x=3.
b) f is concave up on (−5,−1)∪(3,6) and has no points of inflection.
c) f is concave up on (−5,−1)∪(3,6) and has points of inflection at x=−1 and x=3.
d) f is concave up on (−5,−1)∪(3,6) and has a point of inflection only at x=−1.