The y value at such a point is the actual relative

  • No School
  • AA 1
  • 5

This preview shows page 2 - 4 out of 5 pages.

The y-value at such a point is the actual relative extreme value, while the x-value is the location at which the extreme value occurs For parabolas, the relative extremum is the coordinate of the vertex and can be found algebraically. For most other functions, these extreme values require the use of calculus or a graphing calculator. Example 3 Find the coordinates of all relative extrema for the following functions using a graphing calculator. (a) 4 2 ( ) 7 6 f x x x x ± ² (b) ³ ´ 2/3 ( ) 3 4 2 U x x ± ± (c) 2 ( ) g x x x x ± Functions like the ones in the previous example have graphs that are curvy, meaning they increase or decrease at different rates. We are all familiar with speed. For instance, if you drive a total distance of 130 miles in 2 hours, your average speed, or average rate of change (AROC), would be ࠵?࠵?࠵? ࠵?࠵?࠵?࠵?࠵? = ࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵? ࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵? ࠵?࠵?࠵?࠵?࠵?࠵?࠵? ࠵?࠵?࠵?࠵? = 130 ࠵?࠵? 2 ℎ࠵? = 65 ࠵?/ℎ This doesn’t mean, necessarily, that you had to be traveling at 65 mph the entire time, for you likely went slower at times, and therefore, faster than 65 mph at other times. We can do the same calculation for functions over x intervals, talking about how “fast,” on average, the y - values change on the interval. In the above example, if we let the function d(t) represent the distance you traveled, in miles, and let t represent the time spent on your trip, in hours, the calculation looks like this: ࠵?࠵?࠵? ࠵?࠵?࠵?࠵? ࠵?࠵? ࠵?ℎ࠵?࠵?࠵?࠵? ࠵?࠵? ࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵? = ࠵?(2) − ࠵?(0) 2 − 0 = 130 ࠵?࠵? 2 ℎ࠵? = 65 ࠵?/ℎ
Image of page 2

Subscribe to view the full document.

Average Rate of Change on a Closed Interval Example 4 Sketch the function (without a calculator) ³ ´ 2 ( ) 4 f x x ± , then find the average rate of change on the following closed intervals.
Image of page 3
Image of page 4

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern

Ask Expert Tutors You can ask 0 bonus questions You can ask 0 questions (0 expire soon) You can ask 0 questions (will expire )
Answers in as fast as 15 minutes