Honors Precalculus March 22 – 27, 2018 Mr. Agnew Rates of Change Honors Precalculus March 22 – 27, 2018 Mr. Agnew

Essential Question Essential Vocabulary 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 The rate of change of a given function from a to b is given by: Average Rate of Change: rate at which the values of a function change as the variable changes. Example: Average speed

Rates of Change Rates of change for linear functions are constant (rate of change = slope). Rate of change varies for all other functions. Let’s find the rates of change for different functions… examples.

Average Rate of Change The average rate of change gives the slope of a SECANT line between x=a and x=b. Let’s examine the graph of the AROC and a calculus expression known as the DIFFERENCE QUOTIENT.

Homework: 3/26/18 page 90 – 92 #61, 65, 68 77(c,d,e,f), 81 – 87 (Odd; only part a: Use Difference Quotient to find the AROC from a to a+h)

Increasing and Decreasing A function is said to be increasing when the graph has a positive slope. In other words, the graph is rising. A function is said to be decreasing when the graph has a negative slope. In other words, the graph is falling.

Extreme Values An extreme value is a maximum or minimum value of a function Local extrema vs. absolute extrema Maximum values occur when the function changes from increasing to decreasing Minimum values occur when the function changes from decreasing to increasing.

Homework: 3/27/18 Worksheet Provided