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

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.

[James Tursa]

What have you done so far? What specific problems are you having with your code?

[Peter Pyrka]

Honestly the only thing Ive done is record each equation and the values into matlab. If you can give me advice on how to take on each step of this lab it would be great because from my class I don't really know where to start or how to tackle each step(specifically like what commands to use or computing the points of forms like it asks in #2 and #7). I understand this is asking a lot but any help would be amazing !

[Walter Roberson]

See plot() and fplot() and fsurf() and fimplicit()

[Peter Pyrka]

I understand that helps me plot the equations, but how do i find points of the form(A,y)?

[Walter Roberson]

solve(4*x+2*y-x*y+3*x^2-5*y^2+5,y) and substitute x=A