How to plot a graph of the derivative of a function.
The 'derivative' or 'derived function' evaluates to the gradient of the original function at any given 'x' value.
Derivative graphs can tell you a lot about a function. The following graph shows the original function (blue) and its derivative (red) plotted together:
Consider the function plotted in blue above:
Using the rules of calculus, the derived function is:
For any 'x' value, the 'y' value of the derived function equals the gradient of a tangent to the original function at that point. Here are some brief observations from the graph above:
Also, the derived function 'x - 1' is a straight line, which indicates that the gradient of the original function increases at a constant rate as 'x' increases.
For any function that can be graphed in Maths Helper Plus, a derivative graph can be calculated and plotted automatically. This works even if you don't know how to calculate the derivative using algebra.
Maths Helper Plus can graph the derivative of a function, as well as create a table of derivative values.
Step 1 Start with an empty Maths Helper Plus document
If you have just launched the software then you already have an empty document, otherwise hold down ‘Ctrl’ while you briefly press the ‘N’ key.
Step 2 Graph your function
If the graph of the function does not appear, you need to adjust the
Step 3 Display the options dialog box for the function
Carefully point to the plotted function graph line with the mouse and double click. This will display the function options dialog box, like this:
If a different dialog box displays, click its cancel button to close it, then try again.
As shown in the picture above, click with the mouse to select the 'dy/dx' option. This causes the derivative graph to be displayed.
If you want to display a graph of the second derivative, then select the 'dy/dx' option as well.
To create a table of function and derivative values, select the 'Data Table' tab at the top of this dialog box. Once this tab is selected, click the 'Help' button at the bottom of the dialog box for further instructions. Note that you won't need to type anything in the bottom edit box. Leave it as 'y'.
Click the OK button to close.