Theory and Examples

Estimating reciprocals without division You can estimate the value of the reciprocal of a number a without ever dividing by a if you apply Newton’s method to the function For example, if a = 3,the function involved is

a. Graph Where does the graph cross the x-axis?

b. Show that the recursion formula in this case is so there is no need for division.

Calculus notes for the week of 10/3/16 4.1 Maxima and Minima and 4.2 What Derivatives Tell Us 15 10 5 01 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 -5 -10 -15 f has a local maximum at c if f(c) > f(x) for all x sufficiently close to c. f has a local minimum at c if f(c) < f(x) for all x sufficiently close to c. We see that, if f is differentiable at a local...