Question

Suppose the tangent line to the curve

y = f(x)
at the point
(1, 1)
has the equation
y = 7 − 6x.
If Newton's method is used to locate a solution of the equation
f(x) = 0
and the initial approximation is x1 = 1, find the second approximation x2.

Answer 1

x2 = 7/6

Explanation:

You want the second approximation using Newton's method, given that the first approximation is x1=1 and the function tangent at x=1 is y=7-6x.

Newton's method

Newton's method approximates the function by its tangent line at the point (x, f(x)). That is, the second approximation is the x-intercept of the tangent line y = 7 -6x. That value of x is ...

0 = 7 -6x

6x = 7 . . . . . add 6x

x = 7/6 . . . . divide by 6

The second approximation is x2 = 7/6.