(10%) 4. Let g(x, y, z) be a function defined on R³ with continuous partial derivatives. Suppose that Vg(2, 1, 3)² = 36

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10 4 Let G X Y Z Be A Function Defined On R With Continuous Partial Derivatives Suppose That Vg 2 1 3 36 1 (33.13 KiB) Viewed 27 times

(10%) 4. Let g(x, y, z) be a function defined on R³ with continuous partial derivatives. Suppose that Vg(2, 1, 3)² = 36 and g.(2, 1, 3) > 0. Moreover, the trajectories of the two curves Fi(s) = (28, 28²-s, 1+2s) and r(t) = (2e', cost, 3-t + 5t²) lie on the level surface g(x, y, z) = 0 completely. . (A) Find Vg(2, 1, 3) ● (B) Suppose that f(x, y, z) is a function defined on R³ with continuous partial derivatives such that f(2,1,3) ≤ f(x, y, z) for every point (x, y, z) on the level surface g(x, y, z) = 0. If f(2, 1, 3) = 4, Vƒ(2, 1, 3)2 = 9 and f,(2, 1, 3) > 0, estimate the value of f(2.01,0.95, 2.98) by the linear approximation of fat (2,1,3).