Try interactive SELFTEST on these terms ? 
Definition 1  A CRITICAL VALUE (CV) of a function f is a number c for which either:  


Definition 2  Two numbers are NEARBY if NO CRITICAL VALUE lies between them. 
Definition 3  A RELATIVE MAXIMUM (REL MAX) of f is a number x=a for which f(a) f(x) for all nearby numbers x. (A, E, and J in figure below). 
Definition 4  A RELATIVE MINIMUM (REL MIN) of f is a number x=a for which f(a) f(x) for all nearby numbers x (A, C, F, and L in figure below). 
Definition 5  A RELATIVE EXTREMUM of f is a number x=a which is either a relative maximum or a relative minimum of f. 
Definition 6  A LEDGE VALUE (LV) of f, or simply LEDGE, is a number x=a which is a critical value but NOT a relative extremum. In the figure below, ledge values occur at G (horizontal ledge) and K (vertical ledge). 




Definition 9:  A graph or function is called CONCAVE UP in an interval if the graph lies ABOVE it's tangents in that interval. Similarly, this graph is called CONCAVE DOWN if it lies BELOW it's tangents. Concavity is illustrated in the graph shown above 

(e.g., use a mouse on intervals [B,C] or [C,D] in the figure above)  

(e.g., use a mouse on intervals [E,F] or [F,G] in the figure above) 
Definition 11:  A CANDIDATE of f (or 2nd order Critical Value) is a number x = k at which either f "(k) = 0 or f "(k) is undefined. It is not always possible to distinguish candidates by the shape of a graph, but points A, B, D, F, H, K and L are candidates above. 
Definition 12:  An INFLECTION POINT (IP) is a candidate at which f "(x) changes sign, and hence (see Facts 10a/10b) concavity changes. Points B, D, G, and K above are IPs, as well as candidates. 

There will be 3 tests available, as follows:
IIIA. Graph test (stated below)
IIIB. 1^{st} derivative test (see text Pg.172 and below)
IIIC. 2^{nd} derivative test (see text Pg.189 and below)

Calculate f '(x) at 2 nearby test values, x = b and x = d, with b c d: see figure above. 
If f '(b)O , and f '(d)O , then x = c is a relative maximum; again, see GRAPH A above. 
If f '(b)O , and f '(d)O , then x = c is a relative minimum; again, see GRAPH B above. 
Otherwise, x = c is a ledge; again, see GRAPH C above. 
Calculate f "(x) at x = c. 
If f "(c) < 0 , then x = c is a relative maximum; again, see GRAPH A above. 
If f "(c) > 0 , then x = c is a relative minimum; again, see GRAPH B above. 
If f "(c) = 0 , then x = c could be a max, min, or ledge: use IIIA or IIIB to see which. 
IV. Find f "(x)  
V. Find all candidates (see Definition 9 above).  
VI. Test each candidate k to see whether or not it is an inflection point, as follows:  


