 # Sign charts (extrema & inflection)

We use sign charts to pinpoint important x-values on a given function. They are especially useful when we're not given a visual of the function in a graph.

For example, if I gave you the following function...

...and asked you to pinpoint the x-values for any peaks / valleys (local extrema) or points at which the concavity changes (inflection points), we could use a sign chart to achieve this!

Let's start with creating a sign chart depicting the extrema in this function (with f'(x)). Then, we'll move onto creating a sign chart depicting the inflection points for this function (with f''(x))

## Sign chart for extrema (f'(x))

To create our sign chart for extrema, we must first find f'(x)!

Now, we must set f'(x) to zero, and find the corresponding x-values.

Remember, at the apex of peaks and valleys (a.k.a. local extrema) in our function, the slope is zero...

...because at that point, the slope is a horizontal line!

This results in x = ±1!

Let's place these x-values on our sign chart.

Now, we must plug in x-values less than -1... PAID CONTENT This is the end of the preview. To unlock the rest, get the .