1D Gradient Fields
Watch the YouTube video where I explain this applet: http://youtu.be/TMmM0-KbtrY
We first hear of gradient fields when studying function of more than one variable. Here we look at the 1D equivalent.
In a gradient field (regardless of dimension):
1. The vector always points towards growth (maximum).
2. The vector magnitude is rate of change.
----
Look at the 1D gradient field below.
* Where are the maximums, i.e. where do the vectors point towards each other?
* Where are the minimums, i.e. where do the vectors point away from each other?
Now, select the checkbox Function Points.
*How would you draw the slope field of this function at each of these points?
The slope field is line segments of equal length tangent to the function. So the slope of each segment is the corresponding value of the derivative, i.e. the vector magnitude (divided by Vector scale - see below).
Select the other checkboxes to check your answers.