# Is #f(x)=-2x^3+2x^2-x+2# increasing or decreasing at #x=0#?

##### 1 Answer

Hey there! Simply put, **decreasing** at x = 0. I'll explain why below!

#### Explanation:

You're looking for a characteristic of this function at x = 0, specifically if it's increasing at a point. With this, you need to complete what is known as the **First Derivative Test**.

As with any function, to determine if the function is increasing or decreasing at a point, you need the first derivative.

Differentiating we get:

Now you want to substitute the x value you have into the first derivative.

Simplifying we get:

How do we interpret this? What is the meaning of the first derivative?

The first derivative is the slope/rate of change of a function. Thus, since the slope is **negative**, this means the function is **decreasing**! Conversely, if the first derivative were to turn out **positive**, the function would be increasing!

Hopefully this helps! If you have any questions, feel free to ask and I'll do my best to answer them! :)