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 $\text{\_\_\_\_\_\_\_\_\_\_}$ .

#Calculus

Easy Math Editor

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

@Rishabh Cool. Would you spare some of your time to please post a solution of this.

Akhilesh Prasad - 5 years, 4 months ago

@Rishabh Cool, I have got a issue in this one too so if you will please, see this one too

Akhilesh Prasad - 5 years, 4 months ago

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

Rishabh Jain - 5 years, 4 months ago

The answer given is $(1,\infty)$ .

Akhilesh Prasad - 5 years, 4 months ago

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

Rishabh Jain - 5 years, 4 months ago

@Rishabh Jain – 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.

Akhilesh Prasad - 5 years, 4 months ago

@Rishabh Jain – Finally, found it My solution

Akhilesh Prasad - 5 years, 4 months ago

@Akhilesh Prasad – Should at the end cases be like:
(1) Right Max value<0
(2) Left Min value>0

Rishabh Jain - 5 years, 4 months ago

@Akhilesh Prasad – And shouldn't where you multiplied inequality by (a-2) cases must be made for a-2>0 and a-2<0??

Rishabh Jain - 5 years, 4 months ago

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

Corrected solution part 2

Akhilesh Prasad - 5 years, 4 months ago

@Akhilesh Prasad – So we both are getting the same answer that is not correct!! ... ??

Rishabh Jain - 5 years, 4 months ago

@Rishabh Jain – On a side not, I would wanna ask you are you gonna give JEE this year.

Akhilesh Prasad - 5 years, 4 months ago

@Akhilesh Prasad – absolutely Yes!!

Rishabh Jain - 5 years, 4 months ago

@Rishabh Jain – Hey were u able to open the file i uploaded. coz it was on google drive

Akhilesh Prasad - 5 years, 4 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$