Read stationary points from a derivative graph

The graph crosses the x-axis at $x=0$ and $x=2$. Thus $f^{\prime}(x)=0$ at these two inputs. The graph is above the axis before 0, below it between 0 and 2, and above it after 2. No formula or vertical scale for the derivative is supplied.

Immediately left of 0, at 0 and right of 0, the derivative signs are $+,0,-$. The original function’s tangent rises, is horizontal, then falls. Therefore $x=0$ is a local maximum of $f$, as in the Teacher-filled sign/slope table.

The signs around 2 are $-,0,+$. The original function falls, has a horizontal tangent, then rises, so $x=2$ is a local minimum. The requested outputs are x-coordinates and natures; y-coordinates of $f$ cannot be recovered from the given derivative graph alone. Both source tables and the Teacher conclusions are retained.