# Table of Contents Graphs Of Functions: Relative Minima and Maxima A relative maximum of a function is a y-value of a point that is greater than the y-values.

## Presentation on theme: "Table of Contents Graphs Of Functions: Relative Minima and Maxima A relative maximum of a function is a y-value of a point that is greater than the y-values."— Presentation transcript:

Table of Contents Graphs Of Functions: Relative Minima and Maxima A relative maximum of a function is a y-value of a point that is greater than the y-values of all the neighboring points in a "local region". -2 0 2 4 6 -0.50.511.52 The function shown graphed has a relative maximum  4.4. It occurs at an x-value of  - 0.3.  4.4 The "local region" is within the rectangle. Note the point shown has a y-value > the y-values of all the neighboring points within this rectangle.

Table of Contents Graphs Of Functions: Relative Minima and Maxima Slide 2 Example 1:Approximate the relative maximum of the function, f (x) = - x 3 + x 2 + 3x – 2. Graph the function in the decimal viewing window by pressing, entering the function and pressing. Y = ZOOM 4 Next press 2ndTRACE 4 to start the built-in relative maximum location program. "Left Bound?" will appear.

Table of Contents Graphs Of Functions: Relative Minima and Maxima Slide 3  Next presseleven times to place the tracer star near but to the left of where the relative maximum occurs. Press and "Right Bound?" will appear. ENTER  Next presssix times to place the tracer star near but to the right of where the relative maximum occurs. Press and ”Guess?" will appear. ENTER Next, press three times to place the tracer star near the relative maximum.  Press. ENTER The relative maximum is  1.416.

Table of Contents Graphs Of Functions: Relative Minima and Maxima Slide 4 A relative minimum of a function is a y-value of a point that is less than the y-values of all the neighboring points in a "local region". -2 0 2 4 6 -0.50.511.52 The function shown graphed has a relative minimum  2.2. It occurs at an x-value of  0.95.  2.2 The "local region" is within the rectangle. Note the point shown has a y-value < the y-values of all the neighboring points within this rectangle.

Table of Contents Graphs Of Functions: Relative Minima and Maxima Slide 5 Try:Approximate the relative maximum of the function, f (x) = 2x 3/2 – x 2 to three decimal places. 2ndTRACE 4 to start the built-in relative A relative minimum can be approximated in a similar fashion as a relative maximum described on slides 2 and 3. The major difference occurs after entering the function where is pressed (instead of 2ndTRACE 3 minimum location program. The relative maximum is approximately 1.688.