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.

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