Concavity and Inflection problem, with Trig Functions.

Namaste!

Let where

Find the interval where is concave up, and where is concave down. Finally, list any points of inflection (if there are any).

I began by taking the first derivative of :

(not 100% sure this is correct)

Then I found the second derivative of and got:

To find the critical points I (attempt to) set the second derivative to zero to find where the graph of is concave up or concave down.

Broken into steps:

I try to think of where the graph of

Finally:

So this is the critical point, and possibly a point of inflection.

I test points on a number line on either side of this to find where the second derivative is positive or negative to find where the original function is concave up, or concave down.

A hint was given to use a double angle formula, however I am not very familiar with how to implement these.

However, all of my answers so far have been incorrect. I don't want the solution, I just want to know where I went wrong through this process. Any help would be greatly appreciated. Thanks in advance.

Re: Concavity and Inflection problem, with Trig Functions.

The first derivate is not correct

Re: Concavity and Inflection problem, with Trig Functions.

As you suspect as a possibility, your first derivative is incorrect.

The derivative of is

Re: Concavity and Inflection problem, with Trig Functions.

A 20 minute post, answered in 20 seconds...(sigh).

But in all seriousness, thanks.