- #1

- 16

- 0

Prove that there is a X0 in (0,1] such that f(Xo)=0 & f(X) >0 for 0<=X<Xo (there is a smallest point in the interval [0,1] which f attains 0)

Since f is continuous, then there exist a sequence Xn converges to X0, and f(Xn) converges to f(Xo).

Since 0<=(Xo-1/n)<Xo

Can I just let Xn=Xo-1/n so that 0<=Xn<Xo

So when Xn->Xo, f(Xn)->f(Xo)

I wasn't convinced enough this is the right approach...