= 1. (a) Compute the directional derivative of f(x, z)= = x²z+xz³ at the point (x,z) (-2,4) in the direction û = (3, 1)/√/10. = (b) Find the equation of the tangent plane to the surface z = f(x, y) = x² - y², at the point (1, 2, -3), in the form ax+by+cz = d. - (c) The function f(x, y, z) = x² + 3xy + 2yz + y² − z² – 11 = 0 defines an implicit function <= z(x, y). Show that the point (x, y, z) = (1, 2, 0) yields f = 0. Find az/ax, az/ay and evaluate them at the given point (x, y, z) = (1, 2,0).

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