Inequalities

Need a help please...

I tried but i have stuck here

Is it wrong if I take - 4pi and 12pi as min and max values for the above equation for all alpha?

Please tell me where have I gone wrong...

I would have written
n = ...
To find the actual expression in x, alpha you want to find the min/max value of which satisfies the constraints. Maybe try that for starters?

Ok thanks...

Please tell me where have I gone wrong...

But it doesn't work for all alpha in the range like pi/6

The way you asked it was that alpha was a slack variable that just had to satisfy the inequality constant. So as long as there exists one alpha in that range, the solution is fine.

Edit, when looking at the original question, alpha is fixed (determined by a and b (h?)), not a free variable, which obviously changes the problem. Is the final inequality constraint correct
2pi - alpha <= x <= 2pi+alpha
So for instance if alpha=0, x=2pi and there cannot be a stationary point as the range of x is a point? Or do you want to take the range extreme value as the max value?

Note there appears to be some ambiguity in the question, depending on the sign of B the location of the maximum could be 3pi/2 rather than pi/2. I take it you've accounted for that?

h and b are not the same, and the final ineqality is correct. B=1/2sqrt((a-b)^2+4h^2), which we can take as positive, so the maximum must be at pi/2

The way you asked it was that alpha was a slack variable that just had to satisfy the inequality constant. So as long as there exists one alpha in that range, the solution is fine.

Edit, when looking at the original question, alpha is fixed (determined by a and b (h?)), not a free variable, which obviously changes the problem. Is the final inequality constraint correct
2pi - alpha <= x <= 2pi+alpha
So for instance if alpha=0, x=2pi and there cannot be a stationary point as the range of x is a point? Or do you want to take the range extreme value as the max value?

Note there appears to be some ambiguity in the question, depending on the sign of B the location of the maximum could be 3pi/2 rather than pi/2. I take it you've accounted for that?

I don't undestand what did you mean by the solution is fine as long as there exist one one alpha, cause there can't be a general solution for n as, the number of solutions for n changes as alpha increases or decreses by pi

Thats how I was interpreting the problem last night. Seeing the full question, its obviously incorrect as alpha is fixed by the initial transformation.

what does the final inequality represent?