### Calculus of Powers

Review question

The function $y$ is defined by $y=3x-2x^2$. Write down its derivative and show that, when $x=5$, a small increase in $x$ of $p\%$ causes an increase in the magnitude of $y$ of approximately $17p/7\%$.
Suppose $y = f(x)$, and that $(x,y)$ is on this curve. We now increase $x$ by a small amount $\delta x$, which increases $y$ by a small amount $\delta y$ ($y$ could decrease, in which case $\delta y$ would be negative).
Can you see why $y'$ evaluated at $x$ is roughly $\dfrac{\delta y}{\delta x}$? A diagram might help…