Review question

# Is the gradient function increasing or decreasing on this curve? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

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