Problem

Finding all roots Use Newton's method to find all…

03:38

Problem 22 Easy Difficulty

Finding all roots Use Newton's method to find all the roots of the following functions. Use preliminary analysis and graphing to determine good initial approximations.
$$f(x)=\frac{x}{6}-\sec x \text { on }[0,8]$$

Answer

6.1009,6.7626

Related Courses

Calculus 1 / AB

Calculus Early Transcendentals

Chapter 4

Applications of the Derivative

Section 8

Newton's Method

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Video Transcript

problem Number 22. As for X equals X overs six minus sex picks. That's plot our function in order to visualize our problem. Peace. This is our why access or FX. This is our ex. That's some points in terms of two in both the Y axis and the ax access. Okay. Can use some points in orderto go a little bit more careful and move concise fish. Okay, so now we can see that, uh, or death would look something like this can now see that there are two intersection points and the X axis. Okay, we will. Now, uh, we can now use initial initial points of six and seven. You know what? Just tow. This will be good industry points as we can deduct from the half we've just drawn. Okay, So initial wins six and seven. Okay. We will use Newton's method, which is which is given by the formula. X N plus one equals xn minus f xn over f dash off X n. Since our function is X over six minus take X Therefore, our first derivative of the function would be won over six minus sign X over course. I in X power to 20 calls on X Forward to We can now apply the Newton's method for both points. Using a table method toe. Help us with our iterations and acts of and f of x deaf dash X Until use this address for both Oh, it's points period. You can split it in half a news. Use it for both, for both energy points. So for the our initial gas off six, it has an FX negative 0.41 And then after that of actual 0.469 seven second Jason, 6.88 three Now get to 0.5 We see 6785 onto the 3rd 16.7 Negative. 0.0 is you. You eat 0.3542 This will be our final iteration for this initial guess. Okay, now, on to the second initial point off seven, we'll have an S of actual negative 0.15 You could just 0.989 to secondly, tradition 6.8 three eight forced, and it's zero point 03708 negative 0.563 Third Depression 6.7726 maybe 20.4 to 7 negative 0.43695 Fourth Iteration 6.76 to 899 and it's 0.84 negative 0.4197 on our final edition will give us a value for the X event. 6.76 26 by eight Best of zero point 0000 Okay, this would be for things problem.

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