Prove that $|f'(x)| \le \frac{A}2 \forall x \in [0,1] $
111186
Proving that if $|f''(x)| \le A$ then $|f'(x)| \le A/2$
20192
Prove that: $(f(x))^{2} + (f'(x))^{2} \leqslant \max(a,b)$ where $(a,b) \in \mathbb{R}^2$
1371
Prove that $f'(a)=\lim_{x\rightarrow a}f'(x)$.
157577
Prove that $\lim_{x\to y} \frac{d(x, F )}{|x−y|} = 0$ for a.e. $y \in F$.
34136
$f$ is differentiable in $[0,1]$ ,$\sup_{x\in[0,1]}|f'(x)| \le M\lt+\infty $
17646
If $\frac{f(x)}{x}$ is decreasing in $(0,\infty)$, prove that $f(a+b) \leq f(a) + f(b)$ for $a,b >0$
101918
Let $f(x)=ax^2+bx+c$ where $a,b,c$ are real numbers. Suppose $f(-1),f(0),f(1) \in [-1,1]$. Prove that $|f(x)|\le \frac{3}{2}$ for all $x \in [-1,1]$.
84313
$|f(z)|\le 1-|z|\forall z\in D$, we need to show $f\equiv 0$
101778
Show that there is $\eta\in(0,1)$ with $f''(\eta)=f(\eta)$
28007
Assuming: $\forall x \in [0,1]:f(x) > x$ Prove: $\forall x \in [0,1]:f(x) > x + \varepsilon $
49408
Proof of the derivative of ln(x)
62524
Showing that $\int\limits_{-a}^a \frac{f(x)}{1+e^{x}} \mathrm dx = \int\limits_0^a f(x) \mathrm dx$, when $f$ is even
64485
Proving $\displaystyle\lim_{h\to0}\frac{f(x+h)-2f(x)+f(x-h)}{h^2}=f''(x)$
3110
Prove $\frac{1}{\sqrt{x}}\geq \frac{\ln x}{x-1}$
111470
Proof of differentiability of $f(x)$
97253
How prove $e^x|f(x)|\le 2$ if $f(x)=\int_{x}^{x+1}\sin{(e^t)}dt$
121771
Proof $f(x)\equiv 0$