Find the gradient of f(x, y) = x² + 2y² – 3x + 2y at the point (x, y) in the direction making an angle α with the positive x direction. What is the value of the gradient at (2, –1) when α = 1/6π? What values of a give the largest gradient at (2, –1)? The level curve of f (x, y) through (2, –1) is given by f(x, y) = f(2, –1). This defines the relationship between x and y on the curve. Show that the tangent to the level curve at (2, –1) is perpendicular to the direction of maximum gradient at that point and parallel to the direction of zero gradient.