4.1 Applications of the First Derivative
Determining intervals where a function increases or
decreases from a graph
Identifying Critical Numbers of a function
Determining intervals where a function increases or
decreases from an algebraic definition
When given a graph:
Find the largest open intervals where f is
increasing
(intervals
separated by semicolons)
Find the largest open intervals
where f is
decreasing
(intervals separated by semicolons)
When no graph is given:
The procedure to follow in determining the intervals where f
increases or decreases is the following:
Find all values of x for which
f’(x)= 0 of f’(x) DNE.
Identify the open intervals determined by these x values.
Choose a test value, c, in each of these intervals.
If f’(c) > 0, f is increasing in the interval.
If f’(c) < 0, f in decreasing in the interval
Let f(x) = x
2
+ x – 20,
Find the largest open intervals where f is increasing
(intervals separated by semicolons)
Find the largest open intervals where f is decreasing
(intervals separated by semicolons)
NOTE: If none, enter none
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 Spring '08
 VAUGHN
 Calculus, Algebra, Critical Point, Derivative, Fermat's theorem, largest open intervals

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