I am really lost with this lab I have for Calculus 3, anyhelp would be great!

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Peter Pyrka 2019-10-31

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https://ww2.mathworks.cn/matlabcentral/answers/488432-i-am-really-lost-with-this-lab-i-have-for-calculus-3-anyhelp-would-be-great

评论： Walter Roberson 2019-10-31

Given:

f(x,y) = 4x + 2y - xy + 3x^2 -5y^2 +5
A = 2.4 , (B,C) = (-4.9,-6.8)
g(x,y,z) = y + z + 2xy + 2xz + 6yz - x^2 - 5z^2 - 4

Your code should consist of the following:

1. A sketch of the curve(s) satisfying f(x, y) = 0.

2. Compute the points of the form (A, y) that are on the curve. 1

3. Find an equation of the tangent line to the curve f(x, y) = 0 at each point of the form (A, y).

4. Draw a plot of this curve f(x, y) = 0 along with the tangent lines.

5. Using the computer software, find an equation of the form y = h(x) that represents this curve near the point with larger y coordinate, and use Calculus 1 techniques to find an equation of the tangent line at that point. In words, compare and contrast your two results.

6. Draw a sketch of the surface g(x, y, z) = 0.

7. Compute the points of the form (B, C, z) that are on this surface.

8. Find an equation of the tangent plane to the surface g(x, y, z) = 0 at each point of the form (B, C, z).

9. Draw a plot of this surface g(x, y, z) = 0 along with the tangent planes. It will likely be helpful to show one plot for each tangent plane.