7 Multivariate Calculus (a) (2 points) The number of members of a gym in Midtown Atlanta grows approximately as a function of the number of weeks, 35, in the rst year it is opened: f (t) = 100(60 + 582/3. How fast was the membership increasing initially (i.e., what is the gradient of f (if) when t = 0)? (b) Let c be a column vector. Let x be another column vector of the same dimension. (i) (1 point) Consider a iinear function f (x) = ch. Compute the gradient (5% f (x) 1T 2 Hx. Compute the gradient %g(x). (ii) (1 point) Consider a quadratic function g(x) = D 4 4 5%h(x) = 0, what is x 2? Is it a local minimum, maximum or saddle point? (iii) (2 points) Let h(x) = xTHx + ch, where H = [2 0] and c = [1] _ When the gradient