121616949-math.142 - 128 Chapter 6 Applications of the...

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
128 Chapter 6 Applications of the Derivative is usually easy to do. Let’s use 3 2. Now use the tangent line to the curve when x = 2 as an approximation to the curve, as shown in figure 6.17 . Since f ( x ) = 2 x , the slope of this tangent line is 4 and its equation is y = 4 x - 7. The tangent line is quite close to f ( x ), so it crosses the x -axis near the point at which f ( x ) crosses, that is, near 3. It is easy to find where the tangent line crosses the x -axis: solve 0 = 4 x - 7 to get x = 7 / 4 = 1 . 75. This is certainly a better approximation than 2, but let us say not close enough. We can improve it by doing the same thing again: find the tangent line at x = 1 . 75, find where this new tangent line crosses the x -axis, and use that value as a better approximation. We can continue this indefinitely, though it gets a bit tedious. Lets see if we can shortcut the process. Suppose the best approximation to the intercept we have so far is x i . To find a
Image of page 1
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