# Thread: Monotonic Functions and first derivative test

1. ## 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)

but i just cant do it whenever i put some values I get wrong answers please help me out

2. 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)

but i just cant do it whenever i put some values I get wrong answers please help me out
What exactly is your question? Lets say we want to find increasing intervals on $\displaystyle [a,b]$. We apply the first derviative test. We do as you said, we find $\displaystyle f'$ and set it equal to zero (lets say that $\displaystyle c$ 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 $\displaystyle (a,c)(b,c)$. Now we pick two numbers, $\displaystyle a<d<c$ and $\displaystyle c<e<b$ we then find $\displaystyle f'(d),f'(e)$. If the value is positive that is an increasing interval and if it is negative it is decreasing. Does that make sense?

3. 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)

but i just cant do it whenever i put some values I get wrong answers please help me out
Post the particular question that is causing you the trouble

Re: "but i just cant do it whenever i put some values I get wrong answers".