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226 Chapter Three

Figure 3.10 Local maximum
value of a function.

f (x ) 0
0
f (x ) 0
0

Then (x ,y )isa local minimum in the grapà of f. An example
0 0
is shown in Fig. 3.11.

Inflection poinŁ
Let f be a function such that y f(x). Let (x ,y ) be a point on
0 0
the grapà of f, and suppose f is twice differentiable at (x ,y ).
0
0
Suppose the following are botà true:

Figure 3.11 Local minimum
value of a function.