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Q.5) Multivariate functions: (a) For a function f(x, y) = ze zy find all directions il = so that the directional derivative at the point (1,0) in the direction of u is 1, Daf (1,0) = 1. (b) Find the constant a so that the tangent plane to the surface of a = f(x, y) = x3 +y +2 + ay? +2 at (1,2) goes through the origin. (c) For the multivariate function f(x, y.2 ) = x2 ty +2 + yz (i) Find the stationary point(s) of this function. (ii) Find the Hessian matrix. (iii) Find the eigenvalues and eigenvectors of the Hessian matrix at the stationary point(s). (iv) Classify the stationary point (s). (d) Find the extreme values of f(x, y) = ers subject to a + 2y = 3 and x - y = 0