Fluency exercise

# Floppy hair Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

## Problem

This graph shows five curves, $a$, $b$, $c$, $d$ and $e$, which all pass through the origin and the points $(1,2)$ and $(3,0)$. They each have one local maximum between $x=0$ and $x=3$.

Below are the equations of the five curves plus one extra equation. Find the coordinates of the maxima and hence identify which equation goes with which curve.

 $y=x(3-x)$ $y=\sqrt[3]x(3-x)$ $y=\sqrt x(3-x)$ $y=\dfrac{1}{6}x(3-x)(5+x)$ $y=\dfrac{1}{4}x(3-x)(5-x)$ $y=\dfrac{2}{\sqrt[3] 9 -1} \left( \sqrt[3]{9x} -x \right)$

Add a sketch of the missing curve on the same axes.