In first and second derivatives, positive means "upward to the right",
and negative means "downward to the right".
The first derivative f' determines slope of a tangent line, i.e.,
increasing or decreasing.
The second derivative f" determines how the graph is curving, i.e.,
curving concave upward or curving concave downward.
f'(2) = 0 and if f'(x) > 0 when x < 2 and f"(x) < 0 when x > 2.
f'(2) = 0 means that a tangent line drawn to the curve at the point
where x=2 is horizontal.
f'(x) > 0 when x < 2 means that to the immediate left of the point
where x=2, the curve is increasing, i.e., a tangent line drawn there
slopes upward to the right.
f"(x) < 0 when x > 2 means that the curvature to the immediate right
of the point where x = 2 is downward.
The green lines are tangent lines.
Edwin
