The ellipse 4x2+9y2=36 intersects the y-axis at the points A(0,2) and B(0,−2). Which of the following correctly classifies these two points based on the first and second derivatives of y with respect to x?
(a) A and B are both local minima.
(b) A is a local minimum and B is a local maximum.
(c) A is a local maximum and B is a local minimum.
(d) A and B are both local maxima.