Calc04_1 - 4.1 Extreme Values of Functions Greg Kelly...

Info icon This preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon
4.1 Extreme Values of Functions Greg Kelly, Hanford High School Richland, Washington
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
The textbook gives the following example at the start of chapter 4: The mileage of a certain car can be approximated by: ( 29 3 2 0.00015 0.032 1.8 1.7 m v v v v = - + + At what speed should you drive the car to obtain the best gas mileage? Of course, this problem isn’t entirely realistic, since it is unlikely that you would have an equation like this for your car.
Image of page 2
( 29 3 2 0.00015 0.032 1.8 1.7 m v v v v = - + + We could solve the problem graphically:
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
( 29 3 2 0.00015 0.032 1.8 1.7 m v v v v = - + + We could solve the problem graphically: On the TI-89, we use F5 (math), 4: Maximum, choose lower and upper bounds, and the calculator finds our answer.
Image of page 4
( 29 3 2 0.00015 0.032 1.8 1.7 m v v v v = - + + We could solve the problem graphically: On the TI-89, we use F5 (math), 4: Maximum, choose lower and upper bounds, and the calculator finds our answer. The car will get approximately 32 miles per gallon when driven at 38.6 miles per hour.
Image of page 5

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
( 29 3 2 0.00015 0.032 1.8 1.7 m v v v v = - + + Notice that at the top of the curve, the horizontal tangent has a slope of zero. Traditionally, this fact has been used both as an aid to graphing by hand and as a method to find maximum (and minimum) values of functions.
Image of page 6
Image of page 7
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

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