If $f'(x)\not = 1$ for all real numbers $x$, then $f$ has at most one fixed point
18950
Show that $f$ has at most one fixed point
82405
For f continuous on $[0,1]$, show that there exist points $\alpha_k$ such that $\sum \limits_{k=1}^n \frac{1}{f'(\alpha_k)} = n $
138544
For which values of $x$, will $f (x) . f '(x) < 0$?
143354
Prove that there exists $c\in\mathbb{R}$ such that $f'(c)=f(c)$
111485
Let $f(x)$ be continuous on [$0,1$] to $f(x)=0$ for each $x\in[0,1]$
126842
Fixed point in a continuous function
99726
Proving that a function is not a contraction
36402
Prove that $f(x) = \cos(x)$ has a unique fixed point.
151958
How to show $f'(0)$ exist and is equal to $1$?
27948
show that a function $A$ such that $ \rho (Ax,Ay)< \rho (x,y) $ $ \forall x\neq y $ not necessary has a fix point $ (Ax\neq x \space \forall x )$
100740
proof of that a continuous function has a fixed point
2717
Help proving existence of an specific $x_0$ for which $f''(x_0)=0$
28898
Is there a function $f: \mathbb R \to \mathbb R$ that has only one point differentiable?
68165
Find a function $f: \mathbb{R} \to \mathbb{R}$ that is continuous at precisely one point?
100765
If $f'(x) = 0$ for all $x \in \mathbb{Q}$, is $f$ constant?
145017
Example of a function $f$ which is nowhere continuous but $|f|$ should be continuous at all points
81758
Suppose an entire function $f$ is real if and only if $z$ is real. Prove that $f$ has at most $1$ zero.