Write a program that implements the secant method for root finding. Your program is a variant of the Newton-Raphson method, so you should be able to modify the Chapter 6_11 code from Etter & Ingber.

Here is the code to modify:

/*----------------------------------------------------------*/ /* Program chapter6_11 */ /* */ /* This program finds the real roots of a cubic polynomial */ /* using the Newton-Raphson method. */ #include //Required for cin, cout #include //Required for pow() using namespace std; int main() { // Declare objects. int iterations(0); double a0, a1, a2, a3, x, p, dp, tol; // Get user input. cout > a0 >> a1 >> a2 >> a3; cout > x; // Evaluate p at initial guess. p = a0*pow(x,3) + a1*x*x + a2*x + a3; // Determine tolerance. tol = fabs(p); while(tol > 0.001 && iterations

Use your programs for the following physics problem:

Modern Physics: The black body radiation curve has a peak that can be determined by maximizing the Planck radiation formula in frequency form with respect to frequency. The Planck radiation formula is

If we take the derivative of the equation above and set it equal to zero and then substitute x = (hn/kT) we get an expression that reduces to

Solve for the roots of this equation to determine the constant for Wiens law. Use the bisection method and the Newton Raphson method. You will need to replace the function in each program with equation 1 above.

From your value of x determine the constant in Wiens law:

Add a few lines of code to each program to (a) calculate the value of the constant and (b) compare your results to the standard constant (i.e. take a % error) from a your textbook.

I (v, T)