Question

Use Newton's method to find xsubscript6, when xsubscript0 = -7, for the function f(x) = x^2 + 13.5x + 45.

Answer 1

Place this in Physics section....

Answer 2

in other words, start at x=-7 and work thru the tangent line equations 6 times ....

Answer 3

all this is meant for is practice to get you into the feel of the Newton method

Answer 4

\[x _{i+1} = x_{i} - f(x_{i})/f'(x_{i})\]
Since \[x_{0} = -7\]
and f'(x) = 2x + 13.5
\[x_{0+1} = -7 - f(-7)/f'(-7) = -7 - ( (-7)^{2} + 13.5(-7) + 45)/(2(-7) + 13.5)\]
That means that \[x_{1} = -7 - (49-94.5+45)/(-14+13.5)\]
So
\[x_{1} = -8\]
To find \[x_{2}\]
remember that
\[x_{i+1} = x_{i} - f(x)/f'(x)\]
so \[x_{2} = x_{1} - f(x_{1})/f'(x_{1})\]
where \[x_{1} = -8\]
Continue to this process until you find \[x_{6}\]