PPT-Increasing/ Decreasing Functions

Section 42a Definition IncreasingDecreasing Functions A function that is always increasing or decreasing on a particular interval is monotonic on that interval Let be a function defined on an interval. ? Page 1 of 2 Selected comments from the MicroBytes readers… Is your standard of living increasing or decreasing? Decreasing – 5 9% I'm a government employee and the city is tr Objectives. Upon completion of this lesson, you should be able to:. find where functions are increasing or decreasing. A function . f. is . increasing. on (. a. , . b. ) if . f . (. x. 1. ) < . 1  If f0(x)0 forallxin(a;b),thenfis increasing on(a;b).  If f0(x)0 forallxin(a;b),thenfis increasing on(a;b). Denition If f0(x0)=0 ,wesaythatx0isa criticalpoint off. Denition If f0(x0)=0 ,wesayt -3 0 3 (+) a ( (+) If f’(x)0 then function is decreasing on the interval a,bIf f’(x)0 then function is increasing on the interval a,bIf f’( Kevin Buchin. Joint work with . Sander Alewijnse, Maike Buchin. , Andrea . Kölzsch,. Helmut . Kruckenberg. and Michel . Westenberg. . . September 30, 2013. . . . Stopovers in Geese Migration . . 2. x. Domain:. Range:. Continuity:. Increasing/Decreasing:. Symmetry:. Boundedness:. Extrema:. Asymptotes:. End Behavior:. Domain:. Range:. Continuity:. Increasing/Decreasing:. Symmetry:. Boundedness:. Increasing/Decreasing Intervals. AII.7 - The . student will investigate and analyze . functions algebraically . and graphically. Key concepts include. a) . domain . and range, including limited and discontinuous . x. 0.5. x. 2. -2. 2. -1. 0.5. 0. 0. x. 0.5. x. 2. 0. 0. 2. 2. 3. 4.5. As . x . increases. y . decreases. As . x . increases. y . increases. This function is . decreasing when . x. < 0. This function is . Grade Band 9-12. Functions. K-12 Mathematics Institutes. Fall 2010. Placemat Consensus. Functions. Common ideas are written here. Individual ideas . are written here. Individual ideas . are written here. Mean value theorem. Theorem . 3. : Mean Value Theorem for Derivatives. :. If is continuous at every point of the closed interval [a, b] and differentiable at every point of its interior (a, b), then there is at least one point c in (a, b) at . Monotonicity – defines where a function is increasing or decreasing.. A function is monotonic if it is increasing or decreasing on an interval.. d. a. b. c.  . Monotonicity of . Interval. Increasing/Decreasing. “Monotone Sequences”. All graphics are attributed to:. Calculus,10/E. by Howard Anton, Irl Bivens, and Stephen Davis. Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved.”. Introduction. October 17-18, 2016. Mrs. Agnew. Essential Question. How do you find the average rate of change of . a function?. Essential Vocabulary. Average Rate of Change. Function. Function Notation. Average Rate of Change. All slides in this presentations are based on the book Functions, Data and Models, S.P. Gordon and F. S Gordon. ISBN 978-0-88385-767-0. Functions in the Real World. What are the two variables? . Which one depends on which? .