How i find the Local minimum or Maximum Of the Function

[omni]

[(there is an option that there is no Local minimum or Maximum point in this Function)

BUT i need to show the way.

thanks.

 

[Mentallic]

BUT i need to show the way.

Right, so where's your attempt at doing so?

 

[omni]

well i just know that there is no absolute minimum or Maximum in this Function.

In the picture you can see my way

(2cot2x is the same Function)

i know i need to find the Derivative:f'(x)=-4csc^2(2X)

but how i keep on from here to find the Local minimum or Maximum?


thanks

 

[Mentallic]

Sorry, you've jumped from local max/min to absolute max/min, before we continue, could you please clarify whether you're being asked to find any turning points in the function or are you being asked to show that the range of the function is all Reals?

edit: I have a strong hunch that it's the first. Ok so if you were given any function, such as a quadratic, what would be the process to show where the turning point occurs?

 

[omni]

i asked to find the absolute max/min in the range (0;pi/2)

but about local max/min i asked to find any turning points in the function.

can you give me any direction how i find if there any local max/min?

 

[Mentallic]

Sorry, I slept.

Well what happens at a turning point? The gradient is zero there isn't it? So what would be the process to show that a function doesn't have a turning point?

 

[omni]

hi well i Understand and i found there is no local max/min

but still thanks.