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C Roettger, Fall 14 Math 265 Quiz 6A – Solutions Graph of f (x, y) in blue, tangent plane red. Intersection curves of the graph with planes x = x0 and y = y0 green and yellow, respectively. Problem 1 Consider the function f (x, y) = x2 y + y 2 . 5 Find an equation for the tangent plane to the graph of f at P0 = (1, −2). Solution. First, the partial derivatives ∂f 2xy = ∂x 5 ∂f x2 + 2y = . ∂y 5 At P0 , these have the values −4/5 and −3/5, respectively. Finally, we need the value f (P0 ) = 2/5. So the tangent plane to the graph of f at P0 is described by the equation z= 2 4 3 4 3 − (x − 1) − (y + 2) = − x − y. 5 5 5 5 5