Shortcut Functions Problem | JEE Main 2023, Important PYQ

Can You Find The Short Cut In This Functions Problem?

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[Arch]

simple problem, note that both the terms involved are positive, and so we apply the AM-GM as so:
f(x)/2 >= sqrt{(2-x)(3+x)} note that the equality case occurs at x = 1/2. so, our minimum arises there {also note that the min value of -x^2 -x +6 arises at x = 1/2} so we can be sure that this is the overall minima. substituting you will find sqrt{5}

Apply RMS-AM inequality to get:
sqrt{5/2} >= f(x)/2

thus f(x) <= sqrt{10} problem solved. (done mentally)

[Starboy-ki]

please bring set of 30 questions of pyqs of jee mains&adv..

[udayshankar]

Apply R.M.S >= A.M
And directly get the the max value of the function.

[sarojmunot]

Sir aapne Jo trick bataya agar usme under root of alpha-- x^2 + under root of x^2--Beta aaya toh bhi applicable hai

[trijaltripathi]

Sir maxima and minima is also applicable and seemed to be much easier....

[mohdanas]

dy/dx se aur domain ki help se bhi range nikal rhi hia isse ., .

[debalinabose]

Sir ravi subtritution explain kar dejiye

[omkumarsingh]

3:57 but yeh kaise pata lagaye ki thik midpoint of domain set pe hi function ki highest value of range ya output niklega, koi aur bhi toh ho sakta jaha iski value √10 se jyada ho . ?

[wdivyankop]

by diff =o it can solved in 10 seconds!

[Xxtylis]

Aakhri vala ka to domain hi gayab tha😅😅

[jaydeepvishwakarma]

We can also prove it by rolle's theorem

[bshm_y]

Sir why r u disscusing single single Q....plz bring a Q prectice session but not of PYQ's

[Starboy-ki]

sir bhut lag krta hai apka vedio ajkal

[wdivyankop]

sir apki video bhut lag kar rahi hai yar mera device hi lag kar rha ??? pls confirm?

[AdityaMishra-ndcq]

Sir Maine 11 th Kate functions padha hai lekin wo pehla tarike se nhi kr paya only from last method solvable '😢

[mathtricks]

AOD se bhi solve hoga ye very easily

[PhalitSehgal]

Derivative leke zero ke equate kardo lmao.

[AmarSingh-kbfm]

Ab koi bhi ye nhi kahega ki ek din mera bhi comment viral hoga🤣😂

[FacebookCom-tuhr]

I did it in 10 sec with tukka strategy 😂