Basic Question about Newton's Method for Optimization This is a very basic question about Newton's method for optimization, but I cannot seem to find the answer in any of my searches.  If we are using Newton's method (or gradient descent), how do we find a maximum instead of a minimum? Do we just change the sign of the step size to positive instead of negative?

Yes, that's exactly what you do. You can think of this sign change as causing you to perform gradient ascent instead of gradient descent (in the case of using a gradient method). Alternatively, you can think of flipping the sign in a gradient method as performing gradient descent in $-f$. By finding a minimum of $-f$ you find a maximum of $f$. 
Similar reasoning holds for Newton's method (and various other methods as well). 
