Q: Find the gradient of f(x,y) = x^2 + 2y^2 at (1,1). What is the steepest ascent direction and rate? grad f = (2x, 4y). At (1,1): (2, 4). Direction: (2,4)/|(2,4)| = (2,4)/sqrt(20) = (1,2)/sqrt(5). Max rate: |grad f| = sqrt(4+16) = sqrt(20) = 2 sqrt(5).