The figure shows part of a curve passing through \(6\) points \(A,B,C,D,E,F\).

graph with points A to F marked along it

Copy and fill in the following table showing, for each of the points, whether

  1. \(\dfrac{dy}{dx}\) is positive (\(+\)), negative (\(-\)), or zero (\(0\)),

  2. \(\dfrac{dy}{dx}\) is increasing (\(I\)), or decreasing (\(D\)), as \(x\) increases.

\(A\) \(B\) \(C\) \(D\) \(E\) \(F\)
\(\dfrac{dy}{dx}\) is \(+,-,\) or \(0\)
\(\dfrac{dy}{dx}\) is \(I\) or \(D\)

Determine which of (a) and which of (b) apply at the point \(\left(3,3\tfrac{1}{3}\right)\) on the curve \(y=x+\dfrac{1}{x}\).