Let $f$ be a twice differential function on the open interval $(-1,1)$ such that $f(0)=1$. Show that $f'(0) ≥ -\sqrt2$
95288
Prove that, $f'(0) \ge -\sqrt{2}$ for a function $f$ satisfying some conditions on $(-1,1)$.
95684
Show that $g'(x)+g(x)-2e^x=0$
37303
Differential of a smooth function
33523
If $f(0)=0$ and $f'$ is increasing, then $\frac{f(x)}{x}$ is increasing.
107774
Prove $\|x\|_1\le \sqrt n \|x\|_2$
20192
Prove that: $(f(x))^{2} + (f'(x))^{2} \leqslant \max(a,b)$ where $(a,b) \in \mathbb{R}^2$
111756
How do I prove that then $f(x) = 1$ for some $x ∈ [0, 1]$?
97558
Prove that $\left| f'(x)\right| \leq \sqrt{2AC}$ using integration
103030
Proving $\frac{1}{\sqrt{x}}\ge \frac{2}{x+1}$ for $x> 0$
113888
Behavior of derivative near the zero of a function.
132431
Proving $|f'(z)|\leq\frac{\text{Re}(f(z))}{\text{Re}(z)}$
4636
How to show that $f$ is differentiable at $x=0.$
13150
If the derivative of $f$ is never zero, then $f$ is one-to-one
130322
Show that $f(x) = 0$ if $x = 0$ $f(x) = \text{exp}(-1/x^{2})$ if $x \neq 0$ is infinitely differentiable but not analytic at $x_{0} = 0$ `
30860
Prove that $f(x)=0$ in $[-1,1]$.
68538
Show that if $ A(t) \in \mathbb{R ^{n×n}}$ is a differentiable function of $t$ then $\frac{d(det A(t))}{dt}$
69172
$y'=$ ${-x+\sqrt{(x^2+4y)}}\over 2$ , $y(2)=-1$