Which of the following statements are true?(i) Every continuous function f : [a, b] → R has a minimum and maxi-mum point over [a, b](ii) A continuous function f : (a, b] → R can not have a minimum pointover (a, b](iii) Every function f : [a, b] → R which has a maximum point over [a, b]has also a minimum point over [a, b](iv) Every differentiable function f : R → R has a minimum point over RConstruct counterexamples for those that are false. A clear sketch for the false ones

Which of the following statements are true?
(i) Every continuous function f : [a, b] → R has a minimum and maxi-
mum point over [a, b]
(ii) A continuous function f : (a, b] → R can not have a minimum point
over (a, b]
(iii) Every function f : [a, b] → R which has a maximum point over [a, b]
has also a minimum point over [a, b]
(iv) Every differentiable function f : R → R has a minimum point over R
Construct counterexamples for those that are false. A clear sketch for the false ones