A twice-differentiable function h has a first derivative h′ that decreases on (−3,1) and increases on (1,5). Which statement about h is most accurate?
a) h is concave up on (−3,5), so no inflection point occurs at x=1.
b) h changes from concave down to concave up at x=1, so x=1 is an inflection point.
c) h changes from concave up to concave down at x=1, so x=1 is an inflection point.
d) h′ has a relative minimum at x=1, so h must be decreasing there and cannot have an inflection point.