# How do you find the intervals of increasing and decreasing using the first derivative given #y=x/2+cosx#?

##### 1 Answer

**The function is increasing**

**The function is constant**

**The function is decreasing**

#### Explanation:

If

if

If

If

The function

Lets construct a values table for the function

We also know that

To the derivative has a positive value, we must have

To have this we must have

That means exactly the same as

Because

The points where the derivative has the exactly value of zero is when

So, now we have that:

For any

**The function is increasing**

**The function is constant**

So, we must have the function decreasing in all the other possible values

**The function is decreasing**

We can see this in the graph of the function:

graph{y=x/2 + cos(x) [-8.21, 10.14, -3.56, 5.61]}

And here is the derivative:

graph{y=1/2 - sin(x) [-8.21, 10.14, -3.56, 5.61]}