Find the extremum of 3x22y6z2 subject to the constraint x + y z = 1 and verify that it is a minimum value Q 3(b) The linearization of f(x, y, z) about the point P (x0,Yo,Zo) is [6 Marks] L(x, y, z) f(P)+f.(P.)(x-x,)+f,(P,)(y-y)+f,(P)(2-) where the subscripts denote partial differentiation. Find the linearization of f(x,y,z)xxy +3 sinz at the point (2, 1, 0) [7 Marks] Q 3(c) Euler’s method for the differential equation dy/dx = f(x, y) can be summarised as yn+1yfx, y,), where h is the step size. For the initial value problem dy x+y, y(0)=0, first obtain an expression for y,41 and then for h working to 3 d.p.’s 0.2, calculate yi,y2,…,y5, Q 3(d) [6 Marks] Let y(x.)x+c+(x-ct)] Calculatey ‘y a?y

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