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Unformatted text preview: Find parametric equations of the line tangent to the curve x = t 2-1, y = 2 t , z = t 2 + 1 at the point (3 ,-4 , 5). 8. (12 pts.) For f ( x, y ) = x 2 + 3 xy-y 2 , (a) What is the directional derivative of f at (1 , 2) in the direction from (1 , 2) to (4 , 6)? (b) For what unit vector ~u is the direction derivative D ~u f (1 , 2) largest? 9. (14 pts.) Suppose that z = f ( x, y ) where x = 2 u + 3 v and y = 3 u-2 v , and that f has continuous second partials. (a) Find z u in terms of the partial derivatives of f (in other words, in terms of z x and z y ). (b) Find 2 z u 2 in terms of the rst and/or second partial derivatives of f ....
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This note was uploaded on 03/26/2008 for the course MATH 251 taught by Professor Skrypka during the Spring '08 term at Texas A&M.
- Spring '08