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

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

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

\(\dfrac{dy}{dx}\) 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 \(y=x+\dfrac{1}{x}\).