math16B_review_exer1_ans

math16B_review_exer1_ans - - 2 ,- 2) (b) (6 , 2) (c)...

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Math 16B, Section 1 Fall 2005 Sarason ANSWERS TO REVIEW EXERCISES 1 (USER BEWARE) 1. (a) ∂f ∂x = 5 x 4 - 30 x 2 y 2 + 5 y 4 , ∂x ∂y = - 20 x 3 y + 20 xy 3 (b) ∂f ∂x = 12 x - 2 / 5 y 2 / 5 , ∂f ∂y = 8 x 3 / 5 y - 3 / 5 (c) ∂f ∂x = - 2 x y e - x 2 /y , ∂f ∂y = ± x y ² 2 e - x 2 /y . 2. (a) 212 15 (b) - 1 6 (c) 4 105 3. (a) (1 , 2), saddle point; ( - 1 , 2), relative maximum (b) (0 , 0), saddle point; (3 , 3), relative minimum (c) (0 , 0), saddle point; ( 1 8 , 1 32 ) , ( - 1 8 , - 1 32 ) , relative minima (d) (0 , 0), saddle point; ( 1 2 , 1 4 ) , ( - 1 2 , - 1 4 ) , relative minima 4. (a) Maximum value is 16 2, assumed at ( 2 , 2) Minimum value is - 16 2, assumed at (
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Unformatted text preview: - 2 ,- 2) (b) (6 , 2) (c) Maximum occurs at ( 2 3 , 4 3 , 2 ) . 5. ( a 1 + a 2 + + a N N , b 1 + b 2 + + b N N ) 6. a = 1, b =-1 6 7. 80 units of labor, 5 2 units of capital 8. 6 units of labor, 2 units of capital. Make the following corrections in the statements of the exercises 3. (c) f ( x, y ) = 4 x 4 + 2 y 2-xy 3. (d) f ( x, y ) = 4 x 8 + 8 y 4-xy...
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