As you found, .
If , then .
You are told to think of your function as a function of . Therefore, let .
Absolute maxima occur at critical numbers such that or is undefined. Therefore, let's find .
Note can be 'factored' out of the derivative operator because it is a constant (scalar multiple).
Note the use of the product rule because is a product.
As you can see, there are no critical numbers such that is undefined. Now we only have to determine if there are any critical numbers such that .
Since is a constant, we can eliminate it from the equation by dividing the equation by .
I factored from both terms on the right-hand side of the equation. Since , we have: