The derivative h′(x) of a twice-differentiable function h is increasing on the interval (−3,1) and decreasing on the interval (1,4). Which statement about the concavity of h is most accurate?
a) h is concave up on (−3,1) and concave down on (1,4), but there is no point of inflection at x=1 because h′(1) might not be zero.
b) h is concave up on (−3,1) and concave down on (1,4), with a possible point of inflection at x=1.
c) h is concave down on (−3,1) and concave up on (1,4), with a possible point of inflection at x=1.
d) h is concave up on the entire interval (−3,4), so there is no point of inflection on that interval.