# Derivative Practice – Graphs

Another way to practice the derivative rules.

The graph below shows two piecewise defined functions, f and g, each consisting of two line segments.

1. If $h\left( x \right)=2g\left( x \right)-5f\left( x \right)$ calculate ${h}'\left( 3 \right)$
2. If $j\left( x \right)=f\left( x \right)g\left( x \right)$ calculate ${j}'\left( -4 \right)$
3. If $k\left( x \right)={{x}^{2}}f\left( x \right)$ calculate ${k}'\left( 5 \right)$
4. If  $r\left( x \right)=f\left( g\left( x \right) \right)$  calculate ${r}'\left( 0 \right)$
5. Write the equation of the line tangent to the graph of $y=2+f\left( x \right)g\left( x \right)$ at the point  $\left( -4,2 \right)$.

There are a lot more like these that you can ask from  the same graph; or make up your own graph and questions.

Answers:  1. -17/3,     2. 6,     3.  75,     4. -1/3,     5. y = 2 + 6(x + 4)   (Corrected 10-3-12 19:10)