1. (6 points) Let f(ar, y) y3 3r 12y+ 6. Find all critical points of f. Classify

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1. (6 points) Let f(ar, y) y3 3r 12y+ 6. Find all critical points of f. Classify each critical point as a local maximum, local minimum, or saddle point. Compute the value of f at each critical point. 2. Let f(z, y) T2 yat ary 21. (a) (4 points) Find an equation for the tangent plane to the surface 2 f(a, y) at the point where r 33 and y -1. (b) (2 points) Use the linear approximation to f(z,y) at (3,-1) to estimate the value of f(3.1, 1.2). Hint: This makes use of your answer to (b) and is not the eract value of f(3.1, 1.2) 3. (6 points) Find the global maximum and minimum values of f (r, y) 10+2r-r2-y2 on the domain D (a, y) I z2 y2 S 4). 4. (6 points) A light is turned on near the lair of a wolf spider. The brightness of the 18 light is B(z, y) G lumens, with r and y in centimeters. To get away from the light, the spider crawls along a path r(t) so that 2 seconds later, its position is r(2) (2,2) centimeters and its velocity is r (2) J (7,5) centimeters/second. Find the rate of change of brightness in lumens/second along the spider's path at time t seconds

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