Review question

# Can we sketch the curve $y=(x-a)e^x/(x-b)$? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R9898

## Question

The curve $y=\left(\dfrac{x-a}{x-b}\right)e^x,$ where $a$ and $b$ are constants, has two stationary points. Show that $a-b<0 \quad \text{ or } \quad a-b>4.$

1. Show that, in the case $a=0$ and $b=\dfrac{1}{2}$, there is one stationary point on either side of the curve’s vertical asymptote, and sketch the curve.

2. Sketch the curve in the case $a=\dfrac{9}{2}$ and $b=0$.