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3.3 1 st Derivative Test. 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 :
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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.
Ex 2: Find the local min & local max values of the function:
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 @ a Decreasing rate • Dec @ an 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.
Point of Inflection • point where f changes concavity. • where f changes from increasing to decreasing or vice versa. • where f changes sign.
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.