50_Min_Distance.pdf - Finding minimum distances Strategy to...

Info icon This preview shows pages 1–2. Sign up to view the full content.

Finding minimum distances Strategy to tackle the problem (1) Identify the variable to be minimized (here will be the distance D ), and assign symbols to other given quantities. (Give the variables names). (2) Identify the relation that allow us to write down an equality (referred as the primary equation) expressing D in terms of other quantities. (Usually such a rela- tionship can be found from facts in geometry). (3) Reduce the primary equation into one that express D in terms of a single inde- pendent variable. (This may involve the use of a secondary equation). Determine the domain. (Where can the independent variable take values from?) (4) Use calculus (derivative, critical numbers, comparison or appropriate discussions we learn from calculus). Example 1 Which points on the graph y = 4 - x 2 are closest to the point (0 , 2)? Solution: (1) Let D denote the distance from a point ( x, y ) on the graph to the on given point (0 , 2). (2) Express the distance in terms of x and y . From the distance formula, the primary equation is D = ( x - 0) 2 + ( y - 2) 2 . (3) We recognize that
Image of page 1

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

Image of page 2
This is the end of the preview. Sign up to access the rest of the document.
  • Fall '10
  • ThomasKucera
  • Calculus

{[ 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