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)?

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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)?

Mathematics
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no for the function to be continuous the lim f(x) as x->2 should be 5
Maybe if that interval was closed we could use the intermediate value theorem to say no. I don't know what difference it makes.
its not closed

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Well at 2 that creates a jump discont, right

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