$f(0)=0$ and $f'(x)=f(x)^2$
69008
$f'(x) = [f(x)]^{2}$. Prove $f(x) = 0 $
151519
If $f(f(x))=x^2-x+1$, what is $f(0)$?
101778
Show that there is $\eta\in(0,1)$ with $f''(\eta)=f(\eta)$
30204
Prove that $f'(0)$ exists and $f'(0) = b/(a - 1)$
21879
Show that if $\lim_{x\to a}f'(x) = A$ then $f'(a)$ exists and equals A
18905
$f(a)=f(b)=f_{+}'(a)=f_{-}'(b)=0$ and $|f''(x)|\le M$. Show that $|f(x)|\le \frac{M(b-a)^2}{16}$.
86409
Show that $\lim_{x \to +\infty}\left(f(x)+f'(x)\right)=0 \Rightarrow \lim_{x \to +\infty} f(x)=0$
151958
How to show $f'(0)$ exist and is equal to $1$?
103706
If $\{f(0)\}^{2} + \{f'(0)\}^{2} = 4$ then there is a $c$ with $f(c) + f''(c) = 0$
72769
How find this function $xf(x^2)=f(x),x>0$
41226
Find $f:f(xf(x)+f(y))=f(x)^2+y$
99917
What function satisfies $F'(x) = F(2x)$?
57026
$f(0)=f'(0)=f'(1)=0$ and $f(1)=1$ implies $\max|f''|\geq 4$
25467
Prove that $\lim f(x) =0$ and $\lim (f(2x)-f(x))/x =0$ imply $\lim f(x)/x =0$
95684
Show that $g'(x)+g(x)-2e^x=0$
109561
Find $F'(x)$ if $F(x) = \displaystyle \int_{0}^x xf(t)dt$.
96973
If $F(0,0)=0$ and $F(x,y)= \frac{xy}{x^2+y^2}$ for $(x,y)\neq (0,0)$ then $F$ is differentiable at $(0,0)$?