Q42Multiple correct3 Marks24 Dec 2023Let f(x, y) = x^3 + 2x^2 + y^3 + y^2 - 2x + y - 2. Choose the correct option(s) from the following:AThe tangent plane of f at (1,−1)(1, -1)(1,−1) is given by z = -3x - y - 2.BThe tangent plane of f at (1,−1)(1, -1)(1,−1) is given by 3x - y + z - 2 = 0.CThe best linear approximation for f close to the point (1,1)(1, 1)(1,1) is given by 1_{f}(x, y) = 5x + 5y - 6.DThe best linear approximation for f close to the point (1,1)(1, 1)(1,1) is given by 1_{f}(x, y) = x - 5y + 6.EIf T1 is the tangent plane of f at (1,−1)(1, -1)(1,−1) and T2 is the tangent plane of f at (1,1)(1, 1)(1,1), then T1 and T2 intersect at infinitely many points.FIf T1 is the tangent plane of f at (1,−1)(1, -1)(1,−1) and T2 is the tangent plane of f at (1,1)(1, 1)(1,1), then T1 and T2 intersect at only one point.
