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Functions and Their Rates of Change

Functions and Their Rates of Change. Lesson 1.5. Increasing and Decreasing Functions. Consider the function shown below Going from left to right we can think of it as “uphill” or “downhill” for different sections Mathematically we speak of increasing or decreasing.

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Functions and Their Rates of Change

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  1. Functions and Their Rates of Change Lesson 1.5

  2. Increasing and Decreasing Functions • Consider the function shown below • Going from left to right we can think of it as “uphill” or “downhill” for different sections • Mathematically we speak of increasing or decreasing

  3. Increasing and Decreasing Functions • Define increasing • When

  4. Increasing and Decreasing Functions • Define decreasing • When

  5. Interval Notation • We wish to describe intervals where function is increasing or decreasing • Inequality formx < -2.9 • Interval form(-, -2.9) • Graph

  6. Average Rate of Change • Consider two points on a graph of a function • Average rate of change from P1 to P2 is • You should recognize this as the slopeof the line through P1 to P2

  7. Average Rate of Change • Try it out …

  8. Difference Quotient • We have been using • Define this quantity in terms off the function • Create difquo function for calculator

  9. Difference Quotient • Declare f(x) ahead of time for use of this function • Call the function • What does the resulting number represent?

  10. Assignment • Lesson 1.5 • Page 64 • Exercises 1 – 81 EOO

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