MA 227 Midterm: 3-11f-test2
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Find the gradient of the function f (x, y) = x2e xy at the point (1, 0). Find the directional derivative of the function f (x, y, z) = xz2 + yz in the direction of the vector ~v = ~i + 2~j 2~k at the point (2, 1, 1). Find local maximum, minimum and saddle points (if any) of the function f (x, y) = x2. Let z = xy3 1 y . Find equation of the tangent plane at point ( 1, 1). Find linear approximation for the function near point (2, 1). f (x, y) = x2. Let f (x, y) = xy + x2 y and x = st, y = s2 + t. find partial derivatives f. Let f (x, y) = y sin(x) + x2y. Find all second partial derivatives: f yy. xx, f xy, f .
