# The function #f:f(x)=-|x|+1# is decreasing in the interval...?

##### 2 Answers

Decreasing on

#### Explanation:

To determine when a function is increasing or decreasing, we take the first derivative and determine where it is positive or negative.

A positive first derivative implies an increasing function and a negative first derivative implies a decreasing function.

However, the absolute value in the given function stops us from differentiating right away, so we'll have to deal with it and get this function in a piecewise format.

Let's briefly consider

On

On

Thus, on

And on

Then, we have the piecewise function

Let's differentiate:

On

On

We have a negative first derivative on the interval

Decreasing in

#### Explanation:

As a result, since

Graph which also helps

graph{1-|x| [-10, 10, -5, 5]}