Visual Calculus - Graphing a Function and its Derivative

Problem:
Draw the graphs of the function

f(x) = x³ + 8 x² - 3 x + 5

and its derivative. Graphically verify that the function is increasing if and only if its derivative is positive.

Visualization:
The following Mathview Notebook shows the graph of the function f in blue and the graph of its derivative in red.

It is possible for you to change the function. With the mouse highlight the part of the function which you want to change and type in the new terms. You may get an error message but just click with the mouse on the graph. Some examples which you may try:

x⁴-3x²+3
[Type in: x^4-3x^2+3 Note that you will need to position the cursor after you type in a power.]
e^-x²
[Type in: exp(-x^2)]
x^1/3
[Type in: x^1/3]
|x²-4|
[Type in: x^2-4, highlight what you just typed in and then type in|.]