Time by noting that from the derivative formula dy dt

This preview shows page 5 out of 5 pages.

time by noting that: From the derivative formula dy dt dx dt dy dx = you can make the following observations: For horizontal slope where 0 dy dx = the only way this can happen is when 0 dy dt = For vertical slope where dy undefined dx = the only way this can happen is when 0 dx dt = You can use these rules when the problem asks for horizontal and vertical tangent without having to find dy dx . If the problem asks for a generic slope, then you must find dy dx . For example: For the parametric equation 3 3 4cos 4sin x t y t = = Find the equation for the tangent at / 3 t π = Here, you have to find tan( ) dy t dx = − . Hence the slope at / 3 t π = is tan( ) 3 3 dy m dx π = = = You need the point to finish the problem. at / 3 t π = , the point is: 3 3 1 4cos 2 3 3 4sin 2 x t y t = = The problem now becomes a standard Algebra problem: Find the equation for the line having a slope 3 m = − and going through the point 1 3 3 , 2 2 . And you should be able to complete it from here.
Image of page 5

{[ 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