Which of the following statements are true and which are false? I. If 𝑓 ′ ( 𝑐 ) = 0 then  𝑓   has either a local maximum or a local minimum at 𝑥 = 𝑐 . False II. If 𝑓 ( 𝑥 )   is increasing for all 𝑥 ∈ ( − ∞ , ∞ ) , then 𝑓 ( 𝑥 ) has no inflection points. [ Select ] False True   III. There exists a function 𝑓   with a local minimum at 𝑥 = 3   and 𝑓 ′ ( 3 ) ≠ 0 . [ Select ] True False IV. If a function 𝑓 ( 𝑥 )   is increasing on ( − ∞ , 5 )   and decreasing on ( 5 , ∞ ) then 𝑓 ( 𝑥 ) has a critical point at 𝑥 = 5 . [ Select ] True False多重下拉选择题