Solving a Transcendental Equation Using a Numerical or Graphical Method

[SHISHKABOB]

Homework Statement

I have this equation: y = 5(1 - e^-x) and I need to find its root.

Homework Equations

I'm trying to go from Planck's blackbody formula to wien's displacement law by taking the derivative of Planck's blackbody formula with respect to wavelength and then setting it equal to 0 in order to find the maximum wavelength.

The Attempt at a Solution

I know the correct answer because I found an old thread here where they found the intersection between y = x and this equation. However, I don't understand why that gives the correct answer, and I wouldn't know how to write that down as an answer for this homework problem.

 

[LawrenceC]

The transcendental equation would only have 1 variable, namely x. So

x = 5(1-e^-x)

You could add a second equation y=x. Then somehow solve them simultaneously. I would use Newton's method where you take the derivative and approach the solution iteratively.

Write

f(x) = x + 5e^-x - 5

Compute derivative f'(x)

Use recursion relation to determine where f(x)=0

x2 = x1 - f(x1)/f'(x1)

 

[SHISHKABOB]

oh I see now, I was trying to use Newton's method but I had an incorrect understanding of what a transcendental equation was, so I was ending up with very weird results

thank you very much