Q1 (9 points) Let z(x, y) and w(x, y) be smooth functions that satisfy the equations w+w³ + x²yz + 4 = 0, z³+w+xy/w+1=0 and also satisfy 1 z = 1, w = -1 when x = -29 y 2 Using differentials, estimate the value of z(-1.95, -.35) and calculate the percent relative error (the actual value is z(-1.95, —.35) = 0.910558).

Which of the following straight lines are tangent to the curve y = x³ + 4x2 + 7x and passes through the point (0 , 0)? (1) y = 7x (II) y = - 11x %3D (III) y = 11x (IV) 3x + y = 0 (V) 3x - y = 0 Lines I, and V O Lines I , and II Lines II , and IV O Lines III , and IV Only Line I

Calculate y” and y”’

Find the directions of maximum and minimum change of f at the given point, and the values of the maximum and minimum rates of change. f{x, y) = 4y²e*, (2, –4) The maximum change is 32e V37 ; in the direction (-192e“, 32e®); The minimum change is –32e V37 ; in the direction (192e", -32e). The maximum change is 32e6 The minimum change is –32e 6 V37 :; in the direction (192e, -32e ). V37 ; in the direction (-192e6, 32e ); The maximum change is 32e V37 ; in the direction (192e, -32e); The minimum change is –32e V37 ; in the direction (-192e", 32e). The maximum change is 32e V37 ; in the direction (192e ,–32e ); The minimum change is –32e 6 V37 :; in the direction (-192e, 32e ).