If we have the graph of a function \(f\), we can draw a sketch of the graph of \(f’\) by estimating the slope of the tangent to the graph of \(f\) at each \(x\) value. We then plot the points \((x,f'(x))\) in the \(xy\)-plane and connect them by a smooth curve whenever possible. This curve represents the graph of \(f’\).
When you seek to graph the derivative, it is often easiest to first identify the places where the slope of the tangent line is 0. Those are the places where you can hope the sign on the derivative may change.