By applying Rolle's theorem, check whether it is possible that the function f(x)=x^5+x−5 has two real roots.

Question

Answer: (input possible or impossible )

Your reason is that if f(x) has two real roots then by Rolle's theorem:
f′(x) must be (input a number here)
at certain value of x between these two roots, but f′(x) is always (input negative , positive, or zero )

Answer 1

f' = 5x^4+1

Looks like f' > 0 for all x.