Question

TRUE or FALSE?

Answer 1

Which of the following statements are true (T) and which are false (F)? Justify if true and give a counter-example if false.
Suppose that f(x) has domain [1; 3] and is continuous, that g(x) has domain R and is
differentiable, and that h(x) has domain (1; 3) and is differentiable.
YOU DON'T HAVE TO JUSTIFY BUT YOU CAN IF YOU DON'T MIND

(a) There is some a E IR with 1 a 3 such that f has a global maximum at a.
(b) There is some a E IR with 1 < a < 3 such that f has a global maximum at a.
(c) There is some a E IR with 1 < a < 3 such that f has a local minimum at a.
(d) f cannot have infinitely many different local maximum points.
(e) There is some a E IR such that g has a global maximum at a.
(f) g has at least one local extremum.
(g) If h has a local maximum at a 2 (1; 3), then h0(a) = 0.
(h) If h'(a) = 0 for some a 2 (1; 3), then h has a local maximum or a local minimum at a.

Answer 2

i already got a,b ,c,d

Answer 3

stuck on e