APFIVE Second Derivative and Points of Inflection
The twice-differentiable functions $$f$$, $$g$$, and $$h$$ have second derivatives given by:
$$\displaystyle f''(x) = x(x - 1)^2 (x + 2)^3$$
$$\displaystyle g''(x) = x(x - 1)^2 (x + 2)^3 + 1$$
$$\displaystyle h''(x) = x(x - 1)^2 (x + 2)^3 - 1$$
Which of the functions $$f$$, $$g$$, and $$h$$ have a graph with exactly two points of inflection?
A
$$g$$ only
B
$$f$$ and $$g$$ only
C
$$h$$ only
D
$$f$$, $$g$$, and $$h$$
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