title: How does optimize.newton choose x1 if fprime is not provided and it must use the secant method?
body: <p>The <code>scipy.optimize.newton</code> documentation reads: &quot;The Newton-Raphson method is used if the derivative fprime of func is provided, otherwise the secant method is used.&quot; The secant method requires two estimates of the zero of func, x0 and x1. But the examples provided show that <code>optimize.newton</code> works with the secant method when ONLY x0 is input. So I assume <code>optimize.newton</code> is somehow  assigning x1 based off our input of x0, but I'm not sure and am curious to know what's going on. Any clarification would be immensely appreciated!</p>