MAT-2130 Midterm: MATH 2130 App State Spring2016 Test2
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Name: answer key: (12 points) three level curve plots are shown below. I have labeled the levels so you know which curves are higher and which are lower. Thus y + x3 must be the rst graph and x2 y2 must be the second. Also, notice that 10 x2 y2 has level curves x2 + y2 = 10 c which are circles that get smaller as c gets larger. On the other hand, x2 + 2y2 = c are ellipses that get bigger and c get larger (i. e. higher up ). This does match so the last graph is x2 + 2y2. (b) sketch a gradient vector at the points a, b, and c. if the vector is 0, draw an x on the point. Gradient vectors should be perpendicular to level curves and point toward higher ground . None of our gradient vectors are zero vectors, so a, b, and c aren"t critical points.
