Prove that $f(x) = x$ has a solution on [0,1]
17234
Show that a continuous function has a fixed point
21954
A question about $f(x)\equiv 0$
107765
Prove that there exists two roots in $[-1,1]$
2717
Help proving existence of an specific $x_0$ for which $f''(x_0)=0$
111470
Proof of differentiability of $f(x)$
31522
Proving $f$ has at least one zero inside unit disk
13575
Need help for proving that: $f(f^{-1}(A)) ⊆ A$
82597
How to find $ f(x)$ if $f(1-f(x))=x$ for all $x$ $\in \mathbb{R}$
151958
How to show $f'(0)$ exist and is equal to $1$?
125723
Proof of $Y=F_X(X)$ being uniformly distributed on $[0,1]$ for arbitrary continuous $F_X$
85739
Show that $f(x) = 0$ for all $x \in [a,b]$ given $|f'(x)| \leq C|f(x)| $
35889
Suppose that f(0) = f(1) = 0 and x ∈ (0, 1). Prove that there exists c ∈ (0, 1) such that f'(c) = f(x).
4636
How to show that $f$ is differentiable at $x=0.$
19146
Showing that $f$ has exactly one fixed point
54729
Prove that $f$ has a fixed point .
95469
Suppose $f:[0,1] \Rightarrow \mathbb{R}$ is continuous and $\int_0^x f(x)dx = \int_x^1 f(x)dx$. Prove that $f(x) = 0$ for all $x$
97104
Proof that continuous function on $ [0, 2]$ has $f(x) = f(x-1)$ for some $ x$