# Monotonic Functions and first derivative test

• Dec 24th 2008, 09:20 PM
ahmedkamal29
Monotonic Functions and first derivative test
I am stuck with this topic which I just cant understand , I just know how to take derivative of an equation and also to find the critical points , the problem I am having is the increasing and decreasing part , I just cant understand how its done , i know that
f'(x) > 0 (increasing)

f'(x) < 0 (decreasing)

• Dec 24th 2008, 09:25 PM
Mathstud28
Quote:

Originally Posted by ahmedkamal29
I am stuck with this topic which I just cant understand , I just know how to take derivative of an equation and also to find the critical points , the problem I am having is the increasing and decreasing part , I just cant understand how its done , i know that
f'(x) > 0 (increasing)

f'(x) < 0 (decreasing)

What exactly is your question? Lets say we want to find increasing intervals on $[a,b]$. We apply the first derviative test. We do as you said, we find $f'$ and set it equal to zero (lets say that $c$ is the zero). We then set up intervals based on the zeros (lets just say there is one for simplicity) so we should have something looking like $(a,c)(b,c)$. Now we pick two numbers, $a and $c we then find $f'(d),f'(e)$. If the value is positive that is an increasing interval and if it is negative it is decreasing. Does that make sense?
• Dec 25th 2008, 03:45 AM
mr fantastic
Quote:

Originally Posted by ahmedkamal29
I am stuck with this topic which I just cant understand , I just know how to take derivative of an equation and also to find the critical points , the problem I am having is the increasing and decreasing part , I just cant understand how its done , i know that
f'(x) > 0 (increasing)

f'(x) < 0 (decreasing)