b$)$ On the coordinate system below graph the tangent line to the graph of $\backslash ($ f$($x$)\backslash )$ at the point $\backslash ((4,$ f$(4))\backslash ).$ Make sure that you mark $($label$)2$ points on the tangent line based on the information found above $($what is the point that the tangent line passes through? Then use the slope to find the second point$).$

$5.$ Say a water tank is being emptied and the volume, in liters, of the water in the tank after t minutes is given by the function $\backslash (\backslash$mathrm$\{$y$\}=\backslash$mathrm$\{$f$\}(\backslash$mathrm$\{$x$\})\backslash ).$

a$)$ What is the meaning of $\backslash ($ f$(5)=200\backslash )$ in the context of the problem?

b$)$ What is the meaning of $\backslash ($ f$^\{\backslash$prime$\}(5)=-30\backslash )$ in the context of the problem?