Chapter 6, Problem 13P

You must determine the root of the following easily differentiable function,

$e^{0.5x}=5-5x$

Pick the best numerical technique, justify your choice and then use that technique to determine the root. Note that it is known that for positive initial guesses, all techniques except fixed-point iteration will eventually converge. Perform iterations until the approximate relative error falls below 2%. If you use a bracketing method, use initial guesses of $x_l=0\text{ and }{x}_u=2$. If you use the Newton-Raphson or the modified secant method, use an initial guesses of $x_i=\mathrm{0.7.}$ If you use the secant method, use initial guesses of $x_{i-1}=0\text{ and }{x}_i=2$.