# Is #f(x)=-7x^3+x^2-2x-1# increasing or decreasing at #x=-2#?

##### 2 Answers

See explanation.

#### Explanation:

To find if a function is increasing or decreasing at a given point we have to calculate its derivative at the point.

The function is:

so its derivative is:

The value of derivative at

The value of the derivative is less than zero, so the function is decreasing.

Either drawing the graph or taking the derivate

#### Explanation:

Let's start by drawing the graph in Geogebra (an excellent, free geometry program):

Looking at it , it is quite clear that

We can also find this without drawing the graph by taking the derivate, which gives the slope of the tangent in each value of x:

Insert the value

As