# Doubt from application of derivative

Hari Shankar had solved this question by using some theorem I guess , also without that it can be solved by just drawing graph. And checking for all cases

i think Darboux's theorem can be applicable but have doubt we can use it or nt kindly share sir solution @Aryan_2021

please see this problem..

Take a twice differentiable function maybe x^2 and put in the options it will be multiple option i will give the written solution as soon as i reach the home

If you are assuming then please let f(x) will be -x^2 then the whole story will change.

A and C wont change as (-)(-) will become + and for B the point which f'(x) is 0 is 0 in both cases

Yeah,but could you provide some written solution of this question,I think it will help much more.

I think there is some error in question or options as it is defined for all x in question f(x) f''(x) NOT=0