Wednesday

April 1, 2015

April 1, 2015

Posted by **Sam** on Thursday, March 17, 2011 at 2:43am.

- Calculus! -
**Reiny**, Thursday, March 17, 2011 at 9:23amso 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 x-intercept, 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...

Calculus-Newton 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 ...

Calculus - Use Newton's Method with the function f(x)=x^2-2 and initial value Xo...

unique solution - How do I show that the equation x^4 + 3x + 1 = 0, -2 <= x &...

Calculus - Use Newton's Method to approximate the positive root of the function ...

College Math II - Solve by any method. x(x + 1) = 12 I am not sure what method ...

Calculus 1 Newton's Method - Using Newton's method, approximate the root of the ...

calculus - Find the interval which contains a zero for the given function. The ...