Gradient Tracker
Instructions
You can enter any function that you want in the box at the bottom and it will be plotted in green.
The dashed green line shows a tangent to the curve at a particular point.
You can move the green cross to see the tangent at different points or press Animate and watch the tangent change as the green cross moves from left to right. Press Stop to stop the animation.
The blue cross shows the value of the gradient at a particular point. If you select show gradient you can record how the gradient varies. This blue dotted line can be described as the gradient function associated with the green function.
Try some different functions and see what you notice.
Preliminary Question
Note that I have not formally defined what a tangent is, but you may be familiar with the word. Try to give your own definition of a tangent below.
Function 1
Try entering the function and describe what you notice about the gradient.
Function 2
Try entering the function and describe what you notice about the gradient.
Function 3
Try entering the function and describe what you notice about the gradient.
Function 4
Try entering the function and describe what you notice about the gradient.
Function 5
Try entering the function and describe what you notice about the gradient.
Function 6
Now choose a function of your own. Try to predict what the gradient will look like and then see if your prediction fits the data. Describe anything that you notice below.