Math 200 W19 T1 Maple Assignment 3
Due Friday, November 8
Do your assignment in a Maple worksheet, then submit it through Canvas as a .pdf file. Be sure to load all relevant packages every time you open up your worksheet.
1. Letf(x,y,z)=ex2cos(xz)−xyz.
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(a) Calculate the directional derivative of f in the direction of ⃗v = 2, − 3 , 10 .
(b) Calculate the direction in which the directional derivative D⃗vf is minimized at the point P =
(1,1,−1). Determine the minimum value of the directional derivative at this point. To do this, you may have to use the norm command. To calculate the norm of a vector using this, you define a vector v in Maple, and then type norm(v, 2).
2. Calculate an equation for the tangent plane to the surface S : x3 − 2y3 + z3 = 0 at the point (1, 1, 1). Graph the surface and the tangent plane on the same set of axes.
3. Consider the surface S : x2 + 2y2 + 3z2 = 1. Determine all points on S at which the tangent plane is parallel to the P : 3x − y + 3z = 1.
4. Letf(x,y)=(x2+y2)ey2−x2.
(a) Use Maple’s solve command to find the critical points of f(x,y).
(b) Plot f(x,y) in Maple. Make sure your plot shows the function value at the critical points you found in part a). Take a guess as to what the classification of the critical points found in part a) are given the shape of the graph.
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(c) Classify the critical points of f. Do not use the SecondDerivativeTest command in Maple to do this.
(d) Use the SecondDerivativeTest command in Maple to classify the critical points of f.
5. Find 3 numbers x, y, and z that sum to 100 and whose product is as large as possible.
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