Review question

Ref: R7433

Question

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

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 $y=x+\dfrac{1}{x}$.