Problem:
Graphically, find a critical point of the function

f(x) = sin(x + 1).


Visualization:
Using Microcalc:

  1. Choose Beginning Calculus from the initial menu and press .
  2. Use the arrow keys to move to the menu item Extrema - Graphing, press and .
  3. At the prompt F(x) =, enter the formula
    sin(x+1)
  4. Enter the bounds at the prompts
    x_0 = 0 x_1 = 1
    y_0 = 0 y_1 = 1
  5. You get the following graph:

  6. (*)Press and, using the arrow keys, move to Zoom In and press and .
  7. You get a box in the middle of the screen; using the arrow keys and , move the box to contain the relative maximum of the graph.

  8. As seen in the graph above, the box may not contain the line which which appears to contain the relative maximum. To remedy this, press and then ; the box expands and then shrinks horizontally as shown in the following:

  9. Press and you will get the part of the graph which lies in the box:

  10. Continuing in this manner by repeating from (*), you can get a better approximation to the desired critical point.