Question

Does there exist a continuous function and differentiable function f(x) such that f(0)=−3 f(2)=−7 and f(x)−8 for all x in (02)?

Answer: ( yes or no

Answer 1

f(x)is less than or equal to -8

Answer 2

could be a quadratic possibly

Answer 3

but not if f(x) >= -8 or do you mean that other than at 0 and 2 it is <=-8?

Answer 4

either way, you cant jump to -8 and below from the endpoints so I would say that this is not a good function