query: How to use Rolle's Theorem to show that $f$ has at most one fixed point? NOT DUPLICATE
positive_passages.docid: 18950
positive_passages.text: Show that $f$ has at most one fixed point
negative_passages.docid: 13150
negative_passages.text: If the derivative of $f$ is never zero, then $f$ is one-to-one
negative_passages.docid: 48592
negative_passages.text: Prove that $f'$ exists for all $x$ in $R$ if $f(x+y)=f(x)f(y)$ and $f'(0)$ exists
negative_passages.docid: 70304
negative_passages.text: Prove there are $\xi$, $\eta$ with $f'(\xi)f'(\eta)=1$
negative_passages.docid: 12239
negative_passages.text: Holomorphic function with a fixed point
negative_passages.docid: 58664
negative_passages.text: Proving a function is continuous for a fixed variable
negative_passages.docid: 27948
negative_passages.text: 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 )$
negative_passages.docid: 31503
negative_passages.text: Question about Maximum Modulus Principle applied to $|f|+|g|$
negative_passages.docid: 68165
negative_passages.text: Find a function $f: \mathbb{R} \to \mathbb{R}$ that is continuous at precisely one point?
negative_passages.docid: 42638
negative_passages.text: Showing that a function $f$ has a unique fixed point in a metric space.
negative_passages.docid: 82405
negative_passages.text: 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 $
negative_passages.docid: 148266
negative_passages.text: Let $f:X\to X $ be continuous. Does $f $ have a fixed point when $X=[0,1)$ or $X=(0,1) $?
negative_passages.docid: 126842
negative_passages.text: Fixed point in a continuous function
negative_passages.docid: 146572
negative_passages.text: Prove that between any two roots of $f$ there exists at least one root of $g$
negative_passages.docid: 2717
negative_passages.text: Help proving existence of an specific $x_0$ for which $f''(x_0)=0$
negative_passages.docid: 156850
negative_passages.text: Fix-Point Theorem Proof.
negative_passages.docid: 31522
negative_passages.text: Proving $f$ has at least one zero inside unit disk