**A point of inflection is located where the concavity of the function changes, so the answer is (a).**

(b) The first derivative equals zero could be an inflection point, but it doesn't have to be. Consider the vertex of a parabola.

(c) Just because the second derivative is zero doesn't mean you have an inflection point. Consider `y=x^4` at x=0. The concavity does not change but the second derivative is zero.

(d) If the function changes from increasing to decreasing there is a local maximum (assuming the function is continuous), but that isn't necessarily an inflection point. Consider a parabola opening down.

(e) Same as (d); consider a parabola opening up. The point is a local minimum, not necessarily an inflection point.

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