answers_12.5_-12.7_1

answers_12.5_-12.7_1 - 12.5 g =< 2 , 1 > 4. See below for...

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12.5 4. 2, 1 2 1 for tangent line g yx ∇= < −> =− See below for graph. 14. 2,4, 6 0 u f Df < = 20. 2, 2,1 3 u g Dg < > = Increasing most rapidly if the directional derivative is 3 and 22 333 ij k u =+ + is the unit vector. Decreasing most rapidly if the directional derivative is -3 and –u is the unit vector. 24. ,1 2 2 3 for tangent line f < See below for graph. 30. No, the minimum rate of change is 6 which is less than -3 degrees Celsius per foot. 12.6 2.a 3x + 5y + 4z = 18 or a multiple. 10. z = 1 20. 0.1 0.0577 3 df =≈ 28a. L(x,y) = 3x + 4y – 6 48a. proof b. R will be more sensitive to R 1 . 12.7 4. There is a local maximum at
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This note was uploaded on 02/11/2010 for the course MATH 2224 taught by Professor Mecothren during the Spring '03 term at Virginia Tech.

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answers_12.5_-12.7_1 - 12.5 g =< 2 , 1 > 4. See below for...

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