origin. Note here that does change sign (from + to −) as x increases through
0, so that (0, 0) is a point of inflection of the curve. See Figure N4–7.
Figure N4–7Verify the graph on your calculator.
F. GLOBAL MAXIMUM OR MINIMUM
Case I. Differentiable Functions
If a function f is differentiable on a closed interval a ≤ x ≤ b, then f is also
continuous on the closed interval [a,b] and we know from the Extreme Value
Theorem that f attains both a (global) maximum and a (global) minimum on
[a,b]. To find these, we solve the equation f ′(x) = 0 for critical points on the
interval [a,b], then evaluate f at each of those and also at x = a and x = b. The
largest value of f obtained is the global max, and the smallest the global min.
This procedure is called the Closed Interval Test, or the Candidates Test.
Example 16 __
Find the global max and global min of f on (a) −2 ≤ x ≤ 3, and (b) 0 ≤ x ≤ 3, if f