Chapter 6, Problem 18P

Use the secant method on the circle function ${\left(x+1\right)}^2+{\left(y-2\right)}^2=16$ to find a positive real root. Set your initial guess to $x_i=3\text{ and }{x}_{i-1}=0.5$. Approach the solution from the first and fourth quadrants. When solving for $f\left(x\right)$ in the fourth quadrant, be sure to take the negative value of the square root. Why does your solution diverge?