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Please do question 5a and 5b 4. In this problem we analyze the behavior of the...

4. In this problem we analyze the behavior of the polynomial f (x, y) = ax² + bxy + cy? (without using the Second DerivativesPlease do question 5a and 5b

4. In this problem we analyze the behavior of the polynomial f (x, y) = ax² + bxy + cy? (without using the Second Derivatives Test) by identifying the graph as a paraboloid. (a) By completing the square, show that if a + 0, then b 2 4ac - 62 f(x, y) = ax² + bxy + cy? = a [( 2 + Y + 2a 4a2 (b) Let D = 4ac – 62. Show that if D > 0 and a > 0, then f has a local minimum at (0,0). (C) Show that if D > 0 and a < 0, then f has a local maximum at (0,0). (d) Show that if D< 0, then (0,0) is a saddle point. 5. (a) Suppose f is any function with continuous second-order partial derivatives such that f(0,0) = 0 and (0,0) is a critical point of f. Write an expression for the second-degree Taylor polynomial, Q, of f at (0,0). (b) What can you conclude about Q from Problem 4?
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5. @o) is a critical point of f. fe 00)= 0 - fy Coo), Thus, the second degree taylors polynomial Q about (60) is give or bycan easily Q. using problem (4), now we et conclude about 27 A([x+ Fy] 7 1ACB y] (were assumed that Axo) Now if 6 AXO, 4AC-

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