Let f(x, y, z) = x + 2y + 2z (a) Compute the gradient vector at...

 

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Let f(x, y, z) = x² + 2y² + 2z² (a) Compute the gradient vector at the point P = (2,1,1). Also, find an equation for the tangent plane and parametric equations of the normal line to the level surface f(x, y, z) = 8 at P = (2,1,1). (b) Graph the level surface f(x, y, z) = 8, also, the gradient vector and the normal line at point P = (2,1,1). Let f(x, y, z) = x² + 2y² + 2z² (a) Compute the gradient vector at the point P = (2,1,1). Also, find an equation for the tangent plane and parametric equations of the normal line to the level surface f(x, y, z) = 8 at P = (2,1,1). (b) Graph the level surface f(x, y, z) = 8, also, the gradient vector and the normal line at point P = (2,1,1).

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Solution a b Graph of ... View the full answer