derivative and graphs

derivative and graphs - Derivative and Graphs OBJECTIVES 1)...

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Derivative and Graphs OBJECTIVES 1) Find the Intervals on which a function increasing, or decreasing. 2) Find relative extrema of a continuous function using the First-Derivative Test. 3) Sketch graphs of continuous functions Definition: A function f is increasing over an interval I if, for every a and b in I , if a < b , then f ( a ) < f ( b ). (If the input a is less than the input b , then the output for a is less than the output for b .) A function f is decreasing over an interval I if, for every a and b in I , if a < b , then f ( a ) > f ( b ). (If the input a is less than the input b , then the output for a is greater than the output for b .) Increasing and Decreasing Functions. Suppose a function f has a derivative at each point in an open Interval I, then 1. If f ( x ) > 0 for all x in an interval I , then f is increasing over I . 2. If f ( x ) < 0 for all x in an interval I , then f is decreasing over I . 3. If f ( x ) = 0 for all x in an interval I , then f is constant over I . DEFINITION: A critical value of a function f is any number c in the domain of f for which the tangent line at ( c , f ( c )) is horizontal or for which the derivative does not exist. That is, c is a critical value if f ( c ) exists and f ( c ) = 0 or f ( c ) does not exist.
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derivative and graphs - Derivative and Graphs OBJECTIVES 1)...

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