39 Replies
@Apu
Note for OP
+solved @user1 @user2... to close the thread when your doubt is solved. Mention the users who helped you solve the doubt. This will be added to their stats.sinx+cosx = √2 sin(x+π/4)
Now differentiate
$$\frac{\sqrt{2}cos(x+\pi/4)}{1+2sin^{2}(x+\pi/4)}$$
Opt
Denominator is always positive
So check when the numerator is positive
so I am confused in that
what critical points I have to take ?
Graph it man
oh no
graphs again :/
ok I will do it
cosx graph shifted left by π/4
is there any way to find it without graphs ?
Yo I have a method for compositions, but it might not be relevant here ig.
Ah nvm its way too wierd.
did you differentiate
💀
yes
What is it?
what did you get
Its only for visualizations.
Sometimes it helps you predict asymptotes and stuff.
this
is the doubt cleared
But you could also differentiate so its not very useful. Just something I thought while doing functions.
not till now
oh you want this without graphing?
like I want to solve it after the differentiation without graphic
to check when numerator is positive
Just look when cos(x+pi/4) is +ve here.
The denominator will always be positive.
^
you can check by plugging in some values if ur unsure
im not sure what exactly you desire
Cos is +ve in x+pi/4 in (-pi/2,pi/2)
So find the range of x accordingly.
hmm ok
final answer given is
Well ig out of the options, the only one which is in (-3pi/4,pi/4) is the one given
Wait a min lemme check once tho.
allen solution
The actual range would be (-3pi/4,pi/4), but the option B is the only one that is a subset of the same.
must be some domain
Domain in the question is R?
'Cuz of arctan.
yes
Ye, so it can't be domain and stuff.
nothing mentioned about domain
so it must be domain to be guessed from options
The graph of the function in the question is as above. It is increasing in (-3pi/4,pi/4) ig.
+solved @SirLancelotDuLac
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