Rolle’s theorem is not applicable to functionf(x)=|x| in the interval[−3,3] because
f is continuous in(−3,3)
f(3)=f(−3)
f(x)≥0 ∀x in[−3,3]
f is not derivable in(−3,3)
Here, f'(x)=x|x| which does not exist at0∈(−3,3) . Hence, Rolle’s theorem is not applicable tof(x) in[−3,3] asf is not derivable in(−3,3) .