Proving that there exists a solution to $f\bigl(x+\frac1n\bigr)-f(x)=0$
8913
Show that there is $\xi$ s.t. $f(\xi)=f\left(\xi+\frac{1}{n}\right)$
30204
Prove that $f'(0)$ exists and $f'(0) = b/(a - 1)$
27570
Prove $(1-x)\ln(1-x)+(1+x)\ln(1+x)\leq 2x^2$ for $0<x<1$
51659
If $f(0)=0$ then prove that $|f(z)+f(-z)| \leq 2|z|^2$
32506
Prove $kf(x)+f'(x)=0 $ when conditions of Rolle's theorem are satisfied .
126959
Prove $ \frac{1}{x+1} \le \ln(1+\frac{1}{x}) \le \frac{1}{x}$ with usage of the definition of a logarithmic function
31522
Proving $f$ has at least one zero inside unit disk
55693
The functional equation $ f \big( x - f ( y ) \big) = f \big( f ( y ) \big) + x f ( y ) + f ( x ) - 1 $
58041
Prove by Mean Value Theorem $\frac{x}{1+x}0$
48592
Prove that $f'$ exists for all $x$ in $R$ if $f(x+y)=f(x)f(y)$ and $f'(0)$ exists
107727
$m\{x\in [0,1]:f'(x)=0\}>0$
6382
Showing $\frac{x}{1+x}0$ using the mean value theorem
60498
Prove that $\lim_{(x,y)\rightarrow(0,0)} \frac{|x|^{a}|y|^{b}}{|x|^{c} + |y|^{d}}$ does not exist
13270
Prove $\exists \xi \in (a,b):f'(\xi)<1+f^2(\xi)$
111756
How do I prove that then $f(x) = 1$ for some $x ∈ [0, 1]$?
48503
Proving : $ \bigl(1+\frac{1}{n+1}\bigr)^{n+1} \gt (1+\frac{1}{n})^{n} $
112923
Let $f:\mathbb{R}\longrightarrow \mathbb{R}$ a differentiable function such that $f'(x)=0$ for all $x\in\mathbb{Q}$