Problem:
Graphically, find a critical point of the function
f(x) = sin(x + 1).
Visualization:
Using Microcalc:
- Choose Beginning Calculus from the initial menu and press
.
- Use the arrow keys to move to the menu item Extrema - Graphing,
press and
.
- At the prompt F(x) =, enter the formula
sin(x+1)
- Enter the bounds at the prompts
- x_0 = 0
x_1 = 1
- y_0 = 0
y_1 = 1
- You get the following graph:
- (*)Press and, using the arrow
keys, move to Zoom In and press
and
.
- 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.
- 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:
- Press and you will get the part of
the graph which lies in the box:
- Continuing in this manner by repeating from (*), you can get a better
approximation to the desired critical point.