The correct answer is D.
A minimum point of a function $f$ is a point $x_0$ such that $f(x_0) \leq f(x)$ for all $x$ in a neighborhood of $x_0$.
The first derivative of a function at a point gives the slope of the tangent line to the function at that point. If the first derivative is positive at a point, then the tangent line is positive, and the function is increasing at that point. If the first derivative is negative at a point, then the tangent line is negative, and the function is decreasing at that point.
The second derivative of a function at a point gives the rate of change of the slope of the function at that point. If the second derivative is positive at a point, then the slope of the function is increasing at that point, and the function is concave up. If the second derivative is negative at a point, then the slope of the function is decreasing at that point, and the function is concave down.
A minimum point of a function must have a horizontal tangent line, which means that the first derivative must be equal to zero. The second derivative must be positive, which means that the function is concave up.
Therefore, the necessary and sufficient conditions for a point $x_0$ to be a minimum of the function $f$ are that $f'(x_0) = 0$ and $f”(x_0) > 0$.