Practice: Graphing The Derivative of a Function
- Author:
- Allen Walk, Tim Brzezinski
- Topic:
- Derivative, Function Graph
Remember: The derivative of a function f at x = a, if it even exists at x = a, can be geometrically interpreted as the slope of the tangent line drawn to the graph of f at the point (a, f(a)).
Hence, the y-coordinate (output) of the pink point = the slope of the tangent line drawn to the graph of f at the BIG BLACK POINT. (Note that the pink point and the BLACK POINT always have the same x-coordinate.)
Directions
1) Move the point along the graph, left and right.
2) Answer the questions below.
What do you call the pink graph that is formed by moving the black point left and right?
What is the equation of the pink graph?
When the graph of f has a minimum or a maximum, explain what happens to the pink graph.
Directions Continued
3) Change the function in the applet to f(x)=(x^2) - 3.
4) Answer the questions below.
What is the equation of the new pink graph?
When the graph of f has a minimum or a maximum, explain what happens to the pink graph.