Question

Does there exist a continuous function and differentiable function f(x) such that f(0)=−1 f(2)=5 and f(x) less than or equal to −1 for all x in (0,2)?

Answer 1

no for the function to be continuous the lim f(x) as x->2 should be 5

Answer 2

Maybe if that interval was closed we could use the intermediate value theorem to say no. I don't know what difference it makes.

Answer 3

its not closed

Answer 4

Well at 2 that creates a jump discont, right