Posted by Sam on Thursday, March 17, 2011 at 2:43am.
For the function y=(e^2x)+(3x)(10), use Newton's method and the calculator method to find the x value for which y=15. Please show your work so that I can understand the question! Thank you so much!! it means alot!!

Calculus!  Reiny, Thursday, March 17, 2011 at 9:23am
so you are solving
e^(2x) + 3x  25 = 0
let y = e^(2x) + 3x  25
y' = 2e^(2x) + 3
newtons's formula says
X = x  f(x)/f'(x)
where x is your starting x value and X is the new value.
Hopefully your X will approach x, when that happens you have the solution.
X = x  (e^(2x) + 3x  25)/(2e^(2x) + 3)
= (2xe^(2x)  e^(2x) + 25)/(2e^2(2x) + 3)
I made a rough sketch of y = e^(2x) + 3x  25
and noticed that there was an xintercept, which would be your solution, at appr x = 1.5
So I will make that my starting x
X  x
 1.5
1.5096 1.50915695
1.50951695  1.509515688
1.509515688  1.50951688
Wow, got the answer correct to 9 decimal places after only 3 iterations.
The key thing is that you start with an initial guess close to the real number.
Answer This Question
Related Questions
 calculus  Use Newton's method to solve the equation sec x = 4 in the interval x...
 CalculusNewton Method Approximation  Use Newton's method to approximate the ...
 calculus  Hello! Just needed help with understanding this specific question. We...
 Calculus  You are using Newton's method to solve e^x  2. If you first guess is...
 Calculus  Use Newton's Method with the function f(x)=x^22 and initial value Xo...
 calculus  how do i use a taylor series centered at some x value to approximate ...
 Calculus! Please Help!!  The dollar value of a stock x weeks after a change in ...
 unique solution  How do I show that the equation x^4 + 3x + 1 = 0, 2 <= x &...
 Calculus Assignment  Hey there. Okay well I just started first year university ...
 Calculus  Use Newton's Method to approximate the positive root of the function ...
More Related Questions