Let where , so that we want to maximize
Then
The maximum value occurs either where or at Solving we have two non-real solutions, so the maximum occurs at either -1 or +1. Plugging in we see that z = sin x = 1 works, and the maximum value is 0.
Let where , so that we want to maximize
Then
The maximum value occurs either where or at Solving we have two non-real solutions, so the maximum occurs at either -1 or +1. Plugging in we see that z = sin x = 1 works, and the maximum value is 0.