Proof that : $f$ is continously differentiable $\Leftrightarrow |f(x + h) - f(x + t) - l(h - t)| \leq \epsilon |h-t|$
71738
Continuously differentiable function iff $|f(x + h) - f(x + t) - l(h - t)| \leq \epsilon |h-t|$
61799
Prove that $\Vert f(b)-f(a)-f'(a)(b-a) \Vert\leq \sup_{x\in [a,b]} \Vert f''(x)\Vert\Vert b-a\Vert^2$
37850
Does the everywhere differentiability of $f$ imply it is absolutely continuous on a compact interval?
129551
Does $\lim_{h\rightarrow 0}\ [f(x+h)-f(x-h)]=0$ imply that $f$ is continuous?
26388
proof that function is constant
54321
Questions about $f: \mathbb{R} \rightarrow \mathbb{R}$ with bounded derivative
97562
Proving Lipschitz gradient of $f(x)=\sqrt{1+\|x\|^2}$
149739
Prove: $f(t)\leq t+1$
57407
Show that $(x^2 + y^2) \sin\left(\frac{1}{x^2 + y^2}\right)$ is differentiable.
145173
$f: \mathbb{R}^2-\{0\} \rightarrow \mathbb{R}$ is continuously differentiable and $f(\alpha x) = \alpha^2f(x)$, then $x \cdot \nabla f(x) = 2 f(x)$
69378
The derivative of $x!$ and its continuity
149764
If $f$ s twice differentiable and satisfies the following constraints, prove $f'(0)>-\sqrt 2$
126461
Show that $g:I\to\mathbb{R}$ is continuous and $f:(x-x_0)g(x)$ is differentiable
77267
Given $f$ is continuous and $f(x)=f(e^{t}x)$ for all $x\in\mathbb{R}$ and $t\ge0$, show that $f$ is constant function
142812
Prove that $f\in L^1(A)\Leftrightarrow \sum_{n}^{\infty}m(\{ x\in A : f(x)\geq n \}) < \infty$
129856
Show that $f(x)=\frac{x}{1+|x|}$ is uniformly continuous.
152877
Is a monotone differentiable function continuously differentiable?