HH_14_5 - 2 + y 2-z 2 =-1 . Answer: Tangent plane: 4( x 2)...

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(11/11/08) Math 10C. Lecture Examples. Section 14.5. Directional derivatives and gradient vectors in space Example 1 (a) What is the gradient of f ( x , y , z ) = xyz at (1,2,3)? (b) What is the directional derivative of f at (1,2,3) in the direction toward (2,3,4)? (c) What is the greatest directional derivative of f at (1,2,3)? Answer: (a) f (1 , 2 , 3) = a 6 , 3 , 2 A (b) The directional derivative of f at (1 , 2 , 3) in the direction toward (2 , 3 , 4) is 11 3 . (c) The greatest directional derivative of f at (1 , 2 , 3) is 7. Example 2 Give an equation of the tangent plane at the point (2, 2,3) on the hyperboloid of two sheets x
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Unformatted text preview: 2 + y 2-z 2 =-1 . Answer: Tangent plane: 4( x 2) + 4( y 2) 6( z 3) = 0 or 2 x + 2 y 3 z = 1 Interactive Examples Work the following Interactive Examples on Shenks web page, http//www.math.ucsd.edu/ashenk/: Section 14.7: Examples 4, 5, and 6 Lecture notes to accompany Section 14.5 of Calculus by Hughes-Hallett et al. The chapter and section numbers on Shenks web site refer to his calculus manuscript and not to the chapters and sections of the textbook for the course. 1...
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