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Math · Calculus
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l. The length, width, and height of a rectangular chamber are changing at the rate of 3 feet per minute, 2 feet per minute, and foot per minute, respectively. Find the rate at which the volume is changing at the instant the length is 10 feet, the width is 6 feet, and the height is 4 feet. when 5. Use the Chain Rule to find lle. The surface a mountain described by the equation f (x,y) 3y2. If a skier is at the of is point (10, 20, 200), what direction should she move in order to descend at the greatest rate? (a) Find Vf at the point (0, -2). 12 at the point (0,-2) (b) Calculate the directional derivative in the direction of the vector v (c) Find the maximum value of the directional derivative at the point (0,-2) (9. Consider the surface given by x +4y2 10z (a) Find an equation of the tangent plane (in general form) to the surface at the point (2,-2, 2) (b) Find the angle of inclination (in degrees) of the tangent plane at the point (2,-2, 2). Round your answer to nearest tenths. (c) Find a set of parametric equations for the normal line to the surface at the point (2,-2,2). la. Test the function f(x,y) 3xw+ v2 y-5 for relative extrema and saddle points Give answer(s) using ordered triples.

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