Question

True or False Help Please!
If f is decreasing on [0, 2] then f(0)>f(1)>f(2)
If f'(1)>0, then f is increasing on [0, 2]
If f is increasing on [0, 2] then f'(1)>0

Answer 1

what do you think the relation of f(0), f(1) and f(2)

Answer 2

f(0)>f(1)>f(2)

Answer 3

yes. so first one is true

Answer 4

I think the second one is false and the third is true

Answer 5

why do you think second one is false?

Answer 6

Well, just because f'(1)>0, doesn't mean f'(x) at any other x on that interval is >0

Answer 7

yes that's true.

Answer 8

so first true, second false, third true?

Answer 9

yes. you are correct

Answer 10

Ok, thank you

Answer 11

you are welcome:)