Newton's Method to find point on function closest to origin Using Newton's Method, find the coordinates accurate to 6 decimal points of the point on the function y=e^x that is closest to the origin.
Hint

We want the $x$ that yields the minimum value of $D(x)$, the distance between $(0,0)$ and $(x, e^x)$. This is the value for which $D'(x)=0$ and $D''(x)&gt;0$.

Here we would approximate $D'(x) = 0$ using Newton's Method as given by: $$ x_{n + 1} = x_n - \frac{D'(x_n)}{D''(x_n)} $$

Now we just need an expression for $D(x)$ and a first approximation, $x_1$.
Newton's Method will approximate the solution of $ f(x) = 0 $.
Draw a diagram, consider your function, and apply the formula: $$ x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)} $$ until you get your answer