4.3 1st & 2nd Derivative Tests

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Presentation transcript:

4.3 1st & 2nd Derivative Tests

Increasing or Decreasing?: If f  (x) > 0 in an interval, then f is increasing in the interval. If f  (x) < 0 in an interval, then f is decreasing in the interval.

1st Derivative Test c is critical number of f: If f  changes from + to – at c, then f(c) is a local max. If f  changes from – to + at c, then f(c) is a local min.

Concave Up or Down?: Concave up: holds water Inc @ an Increasing rate Dec @ a Decreasing rate

Concave Up or Down?: Concave down: spills water Inc @ an Decreasing rate Dec @ a Increasing rate

Concavity Test f(x) > 0 in an interval, then f is concave up in the interval. f(x) < 0 in an interval, then f is concave down in the interval.

Increasing or Decreasing?: If f  (x) > 0 in an interval, then f is increasing in the interval. If f  (x) < 0 in an interval, then f is decreasing in the interval.

1st Derivative Test c is critical number of f: If f  changes from + to – at c, then f(c) is a local max. If f  changes from – to + at c, then f(c) is a local min.

Concave Up or Down?: Concave up: holds water Inc @ an Increasing rate Dec @ a Decreasing rate

Concave Up or Down?: Concave down: spills water Inc @ an Decreasing rate Dec @ a Increasing rate

Concavity Test f(x) > 0 in an interval, then f is concave up in the interval. f(x) < 0 in an interval, then f is concave down in the interval.

2nd Derivative Test c is critical number of f: If f (c) = 0 & f(c) > 0, then f(c) is a local min. If f (c) = 0 & f(c) < 0, then f(c) is a local max.

HW – 4.3 pg. 302 1, 5 – 10 all, 25 – 49 EOO