Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
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". The function shown graphed has a relative maximum 4.4. It occurs at an x-value of - 0.3. 6 4 4.4 2 -1 -0.5 0 0.5 1 1.5 -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 2 Graphs Of Functions: Relative Minima and Maxima Example 1: Approximate the relative maximum of the function, f (x) = - x3 + x2 + 3x – 2. Graph the function in the decimal viewing window by pressing Y = , entering the function and pressing 4 . Next press 2nd TRACE 4 ZOOM to start the built-in relative maximum location program. "Left Bound?" will appear. Table of Contents Slide 2 Graphs Of Functions: Relative Minima and Maxima Next press eleven times to place the tracer star near but to the left of where the relative maximum occurs. Press ENTER and "Right Bound?" will appear. Next press six times to place the tracer star near but to the right of where the relative maximum occurs. Press ENTER and ”Guess?" will appear. Next, press three times to place the tracer star near the relative maximum. Press ENTER . The relative maximum is 1.416. Table of Contents Slide 3 Graphs Of Functions: Relative Minima and Maxima 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". The function shown graphed has a relative minimum 2.2. It occurs at an x-value of 0.95. 6 4 2.2 2 -1 -0.5 0 0.5 1 1.5 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 Slide 4 Graphs Of Functions: Relative Minima and Maxima 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 2nd TRACE 3 is pressed (instead of 2nd TRACE 4 to start the built-in relative minimum location program. Try: Approximate the relative maximum of the function, f (x) = 2x3/2 – x2 to three decimal places. The relative maximum is approximately 1.688. Table of Contents Slide 5 Graphs Of Functions: Relative Minima and Maxima Table of Contents