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]}