## Question

###### 2. (35 pts) For function f(z,y); define Dif (ro. Yo), where & is a unit vector: (This asks for the definition involving limit_ not "short cut calculational formula_ Illustrate with picture, please: What does it mean (in terms of rates of change)Give calculational formula for Daf (Eo; Yo)_Use yOur calculational formula from part to find the rate of change of f(r,y) = Sry? + y? the direction of the vector (3,3} the point (1,y) = (1,2)In what direction will z - f(I,y) = 1 3ry? + y

2. (35 pts) For function f(z,y); define Dif (ro. Yo), where & is a unit vector: (This asks for the definition involving limit_ not "short cut calculational formula_ Illustrate with picture, please: What does it mean (in terms of rates of change) Give calculational formula for Daf (Eo; Yo)_ Use yOur calculational formula from part to find the rate of change of f(r,y) = Sry? + y? the direction of the vector (3,3} the point (1,y) = (1,2) In what direction will z - f(I,y) = 1 3ry? + y' decrease most rapidly at the point (T,y) = (1,2)- Why? Prove that your computational formula in part holds for any unit vector and any differentiable function f

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