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Increasing and Decreasing Functions

Increasing and Decreasing Functions. Eric Hoffman Calculus PLHS Oct. 2007. Basically means, is the slope positive or negative. Increasing – a function is said to be increasing if f(x 2 ) > f(x1) whenever x 1 < x 2

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Increasing and Decreasing Functions

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  1. Increasing and Decreasing Functions Eric Hoffman Calculus PLHS Oct. 2007

  2. Basically means, is the slope positive or negative • Increasing – a function is said to be increasing if f(x2) > f(x1) whenever x1 < x2 • Decreasing – a function is said to be decreasing if f(x2) < f(x1) whenever x1 < x2 • Note: If derivative at any point x is positive, the function is increasing. If f ’(x) is negative, f(x) is decreasing f(x2) f(x2) f(x1) The function changes from increasing to decreasing at the points where the derivative is equal to zero. f(x1)

  3. What intervals does this function increase or decrease Finding the intervals on which the function switches from increasing to decreasing, etc. The only spot a function will switch from increasing to decreasing is when f ‘(x)=0 or at points where f(x) is undefined Function is decreasing on this interval Function is increasing on this interval Function is decreasing on this interval Function is increasing on this interval

  4. Key Topics • Homework: pg. 176, 1-24 all

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