Calculus based ques( I'm unable to solve)

[lucid heath]

I don't really know how to solve this ques... I tried to solve a bit(the second pic attached).I want to know if I've done the part a and b correct or not..if not then how to do so?

[sterile forum]

Calculus based ques( I'm unable to solve)

[royal mirage]

the table looks good but can you explain your thoughts on b?

[lucid heath]

i guess not. cz My frnd helped ,e solve this and I just wrote it, my brain couldn't get a spit of it..so, I came here to get help on this ques cz I'm blank rn

[royal mirage]

oh.. well i don't think it's right :c

[lucid heath]

so, pls tell me how can I solve this ques in a correct way?

[royal mirage]

i think the minimum will be attained at more like this point

f is symmetric around x=0

so you can know everything about the left side just from the right side

kinda hard to explain but if g is maximized at x for some x>0, then it will be minimized at -x