Q: Let f:[0,inf) -> R satisfy f(0) = 1 and f(x) >= x^2 for all x in [0,inf). Suppose that f is continuous on [0,inf). For which real numbers, c, can we say that the equation f(x) = c must have a solution?
To be honest, I don't even know how to start this problem, all I know is something to do with the intermediate value theorem.
Thank you!
KK