Question 1019847
<pre>
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.

{{{drawing(2000/7,400,-3,7,-8,6,graph(2000/7,400,-3,7,-8,6),
green(line(1,4,3,4),

locate(-3,4,increasing),locate(-3,3.5,over),locate(-3,3,here), 




line(-3,.5,0,3.7),locate(3,3,"concave"),locate(3,2.5,"downward"),locate(3,2,over),locate(3,1.5,here)),

red(triangle(2,0,2,2,2,4)),

circle(2,4,0.15),circle(2,4,0.13),circle(2,4,0.11),circle(2,4,0.09),circle(2,4,0.07),circle(2,4,0.05),circle(2,4,0.03),circle(2,4,0.01),


arc(2,-10,14,-28,90,180), arc(2,-10,7,-28,0,90) )}}}

Edwin</pre>