An implicitly defined curve passes through the point (1,2). At that point the first derivative satisfies dxdy=0 and the second derivative satisfies dx2d2y<0. Which of the following statements is most consistent with this information?
a) The curve has a vertical tangent and is concave down at (1,2).
b) The curve has a horizontal tangent and is concave up at (1,2).
c) The curve has a horizontal tangent and is concave down at (1,2).
d) The curve has slope −5 and is concave down at (1,2).