Calculus!
posted by Sam on .
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!!

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.