Using Newton's Method, determine the first approximation to the solution of:

Question

e^(4x)= 10-2x
starting with x=0
what is x1= ??? P.S. ( the 1 is a subscript )

Answer 1

Let f(x)=e^(4x)-10+2x
We look for the solution(s) of f(x)=0.

Newton's method is essentially
xn+1=xn-f(xn)/f'(xn)

for
f'(x)=4e^(4x)+2

x0=0
x1=x0-f(x0)/f'(x0)
=0 - (1-10+0)/(4*1+2)
=1.5

x2=x1-f(x1)/f'(x1)
=1.25
x3=x2-f(x2)/f'(x2)
=1.018
x4=0.8036
...
x10=0.54669824240377
x11=0.54669824240377