(ll'J points) Recall from calculus that given some flmction 53(3),, the a: you get from solving Ed? = I} is called a critical point ofy this means it could be a minimiser or a masimiser for g. In this question} we will explore some basic properties and build some intuition on why} for certain lom functions such as the MSE loss} the critical point of the lom wl always be the minimiser of the loss. IGiven some linear model at) = "(I for some real scalar of, we can write the the mean squared error (LEE) loss of the model f given the observed data {rhyihi = 1} . . . in. as gs. arr)\"- (c) (2 points) Briefly explain intuitively in words why given a convex function g(r). the critical points we get by solving dg(I) di = 0 minimizes g. You can assume that do is a function of r (and not a constant). (d) (3 points) Now that we have shown that each term in the summation of MSE is a convex function, one might wonder if the entire summation is convex given it's a sum of convex functions. While the answer to this for a multivariable function is out of scope for this course, we can still build some intuitions by focusing on single-variable functions. i. (2 points) Let's look at the formal definition of convex functions. Algebraically speaking, a function g(r) is convex if for any two points (21, g(r1)) and (12, 9(12)) on the function: g(er, + (1 - c)x2) 2