Differentiation - increasing and decreasing functions, stationary points

Consider points on a curve:
 

all points shown	function f(x) is increasing	gradient of tangent is positive	f '(x) > 0
all points shown	function f(x) is decreasing	gradient of tangent is negative	f '(x) < 0
stationary points	function f(x) is stationary	gradient of tangent is zero	f '(x) = 0

• Revisit the big derivative puzzle.
• Movie
• Surfboard applet (trace on)