Show that PROGRAM 1.3.6 implements Newton’s method for finding the square root of c. Use the fact that the slope of the tangent to a (differentiable)
function f (x) at x = t is f (t) to find the equation of the tangent line, and then use that equation to find the point where the tangent line intersects the x-axis to show that you can use Newton’s method to find a root of any function as follows: at each iteration, replace the estimate t by t - f (t) / f ′(t).