The functions are
and
.
The function has a horizontal tangent lines at which the derivative of the function is zero.
\Obsrerve the graph:
\The parabola curve has zeros at
and
.
The other curve has horizontal tangents at
and
.
Therefore, the parabola curve is derivative function
.
Now label the curves
and
.
Graph the functions
and
and horizontal tangents:
.
The zeros of
correspond to the points where the graph of
has horizontal tangent line.
The zeros of
correspond to the points where the graph of
has horizontal tangent line.