**Problem 1**. A picture of the level set is shown below.

Find the equation of the plane tangent to this surface at the point .

**Problem 2**. Find all points on the unit sphere whose tangent planes are parallel to the plane .

**Problem 3**. (a) Compute the directional derivative of at the point in the direction of .

(b) For the same function as in part (a), find the direction in which increases the most at the point . Compute this rate of change.

**Problem 4**. (a) Find all of the critical points for .

(b) Compute the Hessian matrix for and use it to classify the critical points from part (a) as local minima, local maxima, saddle points, or as “unclassifiable.”

(c ) Find where the function achieves its absolute minimum and absolute minimum on the compact set

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