Let f be a function of 2 variables. Use the fact that the gradient of a...

 

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Let f be a function of 2 variables. Use the fact that the gradient of a function is normal (perpendicular) to the level sets of that function to prove the following: the equation of the tangent plane to the graph of f at (a, b, f(a, b)) is z = f (a,b) + fx(a,b) (x a) + fy(a,b)(y- b) (note: the function L(x,y) = f(a,b) + fx (a,b)(x a) + fy (a,b)(y- b) is called the linearization of f at the point (a,b)) Let f be a function of 2 variables. Use the fact that the gradient of a function is normal (perpendicular) to the level sets of that function to prove the following: the equation of the tangent plane to the graph of f at (a, b, f(a, b)) is z = f (a,b) + fx(a,b) (x a) + fy(a,b)(y- b) (note: the function L(x,y) = f(a,b) + fx (a,b)(x a) + fy (a,b)(y- b) is called the linearization of f at the point (a,b))