# Question #e40e5

##### 1 Answer

The function is convex on

#### Explanation:

First, note that

So, we need to find this function's second derivative and then examine when it's positive (the function is convex) and when the second derivative is negative (the function is concave).

We'll use the trigonometric derivatives

To find the next derivative, we'll need to use the chain rule.

It will be easier to think about when this is positive and negative to think about it in basic terms: sine and cosine.

Let's examine each quadrant:

#"QIII"#

Here,

Using a very rough notation in which I only denote positives and negatives for

#f''(x)=(-(-))/(-)=-#

So

#"QIV"#

Here,

#f''(x)=(-(-))/(+)=+#

So

#"QI"#

Wherein

#f''(x)=(-(+))/(+)=-#

And

#"QII"#

Here

#f''(x)=(-(-))/(+)=+#

So