Doubt from differentiability

#1


question 39. @Hari_Shankar sir, @Jagdish_Singh sir , @Shiva_1 sir please share your approches...

#2

#3

sir why you have taken intersection with -|x| as graph will be only outer part then why to find min of function we will have to see the point upto which graph is incresing or decresing..please explain @Sharad sir..

#4

i m getting like that
x^2+2x x(-2,-1)
-1. x\belong (-1,0)
0 in (0,2)
one more branch

#5

@Mayank_2019_1 sir , @Azimuddin_2019 sir please share ur approches thankss

#6

Yeah this is exactly what I got @Sneha_2021
Is there problem in the further part ?

#7

my branch are right na sir?

#8

Yes you are correct