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Unformatted text preview: (partial differentiation) Assume that all the given functions are differentiable. If ( 29 , u f x y = , where cos , sin s s x e t y e t = = , show that: (1) 2 2 2 2 2 s u u u u e x y s t- + = + (2) 2 2 2 2 2 2 2 2 2 s u u u u e x y s t- + = + . 2. If ( 29 z f x y =- , show that z z x y + = . (conditional extreme) 1. Find the point on the plane 2 3 4 x y z + + = that is closest to the origin. (Answer: 2 4 6 , , 7 7 7 ) 2 A manufacturer produces a quantity Q of a certain product and Q depends on the amount x of labor used and the amount y of capital. A simple model that is sometimes used to express Q explicitly as a function of x and y is the Cobb-Douglas production function: 1 Q Ax y - = , where A and are constants with K and 0 1...
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