Problem:
Plot the graph of the relation

x2/3 + y2/3 = 8

and the graphs of the tangent lines to this curve at the points (8,8) and (-8,-8).


Visualization:
Using Microcalc:

  1. Choose Beginning Calculus from the initial menu and press .
  2. Use the arrow keys to move to the menu item Graph F(x,y)=c, press and .
  3. At the prompt F(x,y) =, enter the formula
    x^(2/3) + y^(2/3)
  4. and use the bounds
    x0 = -25 x1 = 25
    y0 = -25 y1 = 25
  5. At the prompt, N = , enter 1 and
  6. at the prompt, c_1 = , enter 8 You will then see the graph of this relation.

  7. Press .
  8. Use the arrow keys to move to Superimpose and press .
  9. At the prompt, F(x,y)=, type in y+x .
  10. At the prompt N= just enter 2 and
  11. at each of the following prompts, enter
    c_1 = -16
    c_2 = 16