Graph of Derivative


Exercises for students
Solve the following on paper and check your answers using the above applet:

Find the set of values of x where the graph of y = x² - 2x is increasing.

Find the set of values of x where the graph of y = 1/x is decreasing.

Find the set of values of x where the graph of y = x³ - x is concave upwards.

Find the set of values of x where the graph of y = 1/(1 + x²) is concave downwards.


Summary

When f'(x) > 0, the the graph of f is increasing.
When f'(x) < 0, the the graph of f is decreasing.
When f'(x) = 0, the the graph of f is stationary.

When f"(x) > 0, the the graph of f is concave upwards.
When f"(x) < 0, the the graph of f is concave downwards.

You can define the function using the following operators:

+	-	*	/	^
	sqrt( )	ln( )	exp( )	pi
	sin( )	cos( )	tan( )
	asin( )	acos( )	atan( )
	sinh( )	cosh( )	tanh( )

Right-click here to download this page, the Java Class File and unzip the Javathings Math Package.

Back to H2 Mathematics Homepage


This applet uses the com.javathings.math package developed by:
Patrik Lundin
patrik@javathings.com
http://www.javathings.com