(a) Consider minimizing the function f(w)=w - 5w+3 using gradient descent (graph of f shown below). Say the current value of w is equal to 5. What is the derivative of f at this point? (show your work) If our step size a = -0.1, what is the new value of w after this single gradient descent update? (b) Say we are part way through SGD for a linear regression problem with p= 1. The current weights are woand w=-. Next we are analyzing (z. y.)= (-1,2). If a = 0.1, what are the new weights after considering this point? Show work for full credit: Wo Explain your result geometrically (include a sketch of the model and a discussion of cost): (c) Assuming n training examples, p features, and T iterations needed for convergence, how long does it take to compute the stochastic gradient descent solution (i.e. w) for linear regression? Answer using big-O notation and briefly explain your reasoning for full credit. In this question we will analyze SGD for a simple (meaning p = 1) linear regression problem. We have n = 2, where (ri, y1)= (2, 1) and (x2, 32)= (1, -1) (plotted below), and wish to fit a linear model to this data. (Note the different scales on z and y below.) . (X2.Y2) = (1,-1) (d) Before we begin SGD, we will set wo - w0. At this point, what is the numerical value of the cost function for linear regression? Our cost function for linear regression is: J(w) == (X,Y) = (2,1) n (hw (x) - y) (e) For SGD we will use a = 1 (learning rate). Using (21, 31), compute the SGD updates (show your work) to find new values for wo and w. Use these new values to draw the current linear model on the plot above and label it M (model 1).