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MAT 136 Exam 3 Review - Applications of Derivatives
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MAT 136 Exam 3 Review - Applications of Derivatives
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MAT 136 Exam 3 Review - Applications ofDerivatives
- ANS-Mean Value Theorem
f'(x) < 0
(i.e. f'(x) is negative) - ANS-Describe f'(x) when f(x) is decreasing.
f'(x) > 0
(i.e. f'(x) is positive) - ANS-Describe f'(x) when f(x) is increasing.
f'(x) = 0 or f'(x) is undefined - ANS-Critical number (or critical value or critical point)
f'(x) changes from negative to positive at critical value
(critical value must be in the domain of f(x)) - ANS-A Relative Minimum on f(x) occurs when...
f'(x) changes from positive to negative at critical value
(critical value must be in the domain of f(x)) - ANS-A relative maximum on f(x) occurs when...
f''(x) > 0 (f''(x) is positive)
or f'(x) is increasing (NOT the same as f'(x) is positive) - ANS-f(x) is concave up when
f''(x) < 0 (f''(x) is negative)
or f'(x) is decreasing (NOT the same as f''(x) is negative) - ANS-f(x) is concave down when
f''(x) changes signs (must be a value in the domain of f(x))
i.e. concavity changes - ANS-Point of inflection on f(x) occurs when...
Relative Maximum by 2nd derivative test
(function is concave down) - ANS-If f''(c) < 0 at a critical point in the domain of f(x), then c is a
Relative Minimum by 2nd derivative test
(function is concave up) - ANS-If f''(c) > 0 at a critical point in the domain of f(x), then c is a
find critical numbers in the given interval. Make a table and evaluate f(x) at the endpoints AND
any critical points in between them.
The extreme value theorem guarantees an abs min and abs max as long as f(x) is continuous
on the interval and the given interval is closed (end points are included with brackets) -
ANS-When finding absolute extrema you must
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