Question

there is only one thng here.

f'(x) > 0 for all x..

so f(x) is an increasing function

now when x is just less than f(1) then the given function tends to -infinity

when x just tends to greater than f(1) the function tends to + infinty
when x is just less than f(2) then the given function tends to -infinity
Thus, there is a root between f(1) and f(2)
same logic will give a root between f(2) and f(3)

so the answer will be 2

I have not explained why there is no root that is nto there between - infinty and f(1) and also between f(3) and infinity.

I hope you can figure that part out :)

this is all abut g.. look carefully

all this after the 2nd line has been done on g!

without actually saying that..

Tx for mentioning that :)