5. Newton's Method in Univariate Case (10 points):

Consider minimizing a convex smooth function of one scalar variable, ). We guess

an initial point, and take a second order Taylor expansion around

f(3) f(3)+(3-pis

-gm) ²5

Show that to minimize the right-hand side, the next value of 5 to guess is:

f'(3)

f" (3)

|8-9 = F"(B(0)).

30 = 3m_

where

(hint: take derivative w.r.t.)

=#880) = f'(()) and

In general, Newton's Method in multivariate case can be found at Slides #44-50 on

https://www.cs.cmu.edu/~mgormley/courses/10701-f16/slides/lecture5.pdf

We strongly recommend you to self-study these slides, as you will need Newton's

Method for the next hands-on project anyway.