This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: maximum of f. If f '(x) < 0 for all x in (a, c) and f '(x) > 0 for all x in (c, b), then c is a local minimum of f. Example: Determine the intervals on which the function is increasing or decreasing and the local maximums and local minimums. Since the domain of f is the same as the domain of f', 4 is the only critical number of f. Testing: By the First Derivative Test, x = 4 is a local minimum. Example: Since the domain of f is the same as the domain of f', 3 and 6 are the only critical numbers of f. Testing: x < 3 f'(10) = 672 f is increasing 3 < x < 6 f(0) = 108 f is decreasing x >6 f(10) = 312 f is increasing By the First Derivative Test, x = 3 is a local minimum and x = 6 is a local maximum. x < 4 f'(0) = 8 f is decreasing x > 4 f'(5) = 2 f is increasing...
View
Full
Document
 Fall '08
 JUNGHENN
 Calculus, Mean Value Theorem

Click to edit the document details