Using the First Derivative to find out more!

Once you take the derivative of a function, you can use that information to create a sign chart that will easily identify for you where the function is increasing or decreasing and local extrema. (Min and max)

If the first derivative is positive, then the function is increasing.
If the first derivative is negative, then the function is decreasing.

For example:

The derivative is:

Now, we will use the first derivative to find the zeros of the function.
First, we will factor out and get This is a difference of 2 squares, so it factors nicely.

Set each piece equal to 0.
Our three zeros equal:

Now, we can make our sign chart and determine when the function is increasing or decreasing.

To determine whether or not the function is increasing or decreasing, we plug in any numbers in between our intervals of zeros to determine if the result it positive or negative.

So, in this function:
Decreasing:
Increasing:

Extrema:
The minimum, there are two are at: x=3 and x=-3.
The maximum is at x=0.

So, we can determine all this information by taking the first derivative of the function, finding the zeros, making a sign chart, then plug in values to determine if negative or positive, (increasing or decreasing).

Hope this was interesting!!

Learn something new every day,

Kori 🙂

About koriproffitt

I am a Senior at Texas State University. I am majoring in Education, and graduate in December!

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