NAME Instructor: Szczesniak Calculus 1 – Assignment 7 – Newton and more Directions: Complete the following problems. Show all of your work and write your answer in the box when possible.
1.Estimate the requested value by using Newton’s method and the given x 1, continuing to x 5. Write your answer for each step in the appropriate place, rounded to six decimal places. Also write down the general formula that you are plugging into your calculator, like for y= x2 x, I would write down x n+1 = x n x 2 n x n 2 x n 1. (5 points each) a) The nonzero zero of y= sin x x2 starting with a guess of x 1 = 0 :5 x n+1 x 2 x 3 x 4 x 5 b) The negative zero of y= 0 :25 x4 x3 + 3 x 12 starting with a guess of x 1 = 3:5 x n+1 x 2 x 3 x 4 x 5 2.Find the critical values, if the function has any. Show all of your work and round to three decimal places when needed. (5 points each) a) y= 9 x2 10x+ 1 b) y= x3 6x 2 + x 5 c) f(x ) = 15 x 2 + 9 x = x = x = 1 d) y= x 3 4 x + 1 e) f(x ) = sin x cos x f )f(x ) = cos 2 x x = x = x = 3.Find the extreme values on the given interval. You may round your answers to three decimal places. (5 points each) a) f(x ) = 2x 3 5x 2 + 3 xon [ 1;2] absolute max of at x= absolute min of at x= b) f(x ) = p x (x 1) on [0 ;5] absolute max of at x= absolute min of at x= c) f(x ) = 4 x2 + 27 x on [1 ;5] absolute max of at x= absolute min of at x= 2