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# Help: Critical points

$f\left( x \right) =\left( { a }^{ 2 }-3a+2 \right) \left( \cos ^{ 2 }{ \frac { x }{ 4 } } -\sin ^{ 2 }{ \frac { x }{ 4 } } \right) +\left( a-1 \right) x+\sin { 1 }$

The set of all values of $$a$$ for which the function above does not posses critical point is $$\text{__________}$$.

Note by Akhilesh Prasad
1 year, 1 month ago

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What's the answer ?? I'm getting a€(0,4)- {1} ........... I might have missed cases because I'm a expert in doing that.. ;-) · 1 year, 1 month ago

The answer given is $$(1,\infty)$$. · 1 year, 1 month ago

How you solved ?? I found f'(x) and ensured that it does not vanish!! And ultimately got the wrong answer!! · 1 year, 1 month ago

Hey were u able to open the file i uploaded. coz it was on google drive · 1 year, 1 month ago

Finally, found it My solution · 1 year, 1 month ago

And shouldn't where you multiplied inequality by (a-2) cases must be made for a-2>0 and a-2<0?? · 1 year, 1 month ago

Considered the cases you told me to, still i am not getting the desired answer. Corrected solution part 1

Corrected solution part 2 · 1 year, 1 month ago

So we both are getting the same answer that is not correct!! ... ?? · 1 year, 1 month ago

On a side not, I would wanna ask you are you gonna give JEE this year. · 1 year, 1 month ago

absolutely Yes!! · 1 year, 1 month ago

Should at the end cases be like:
(1) Right Max value<0
(2) Left Min value>0 · 1 year, 1 month ago

It's too time consuming writing the whole answer so i wanted to attach the scan of the hand written answer, but i dunno how to do it, if you could tell me how to do it. · 1 year, 1 month ago

@Rishabh Cool, I have got a issue in this one too so if you will please, see this one too · 1 year, 1 month ago