Help!

Q: 1) State the intermediate value theorem

2) Suppose $\displaystyle f:[0,1] \rightarrow \mathbb{R} $ is continous on $\displaystyle [0,1] $, $\displaystyle f(0) = 0 $ and $\displaystyle f(1)=1 $.

Prove that there exists a $\displaystyle c \in (0,1) $ such that $\displaystyle f(c) = 1-c $.

My solution:

A: 1) Suppose $\displaystyle f:[a,b] \rightarrow \mathbb{R} $ is continuous on $\displaystyle [a,b] $ with $\displaystyle f(a) < 0 < f(b) $.

Then $\displaystyle \exists c \in (a,b) $ such that $\displaystyle f(c) = 0 $ .

2) ????????????????

Any help would be appreciated thanks