$f(0) = 0$ and $f'(x) = (f(x))^2$ implies $f = 0$.
9270
Differentiable function, with $f'(x)=[f(x)]^2$
72847
Does $f(x)$ is continuous and $f = 0$ a.e. imply $f=0$ everywhere?
85739
Show that $f(x) = 0$ for all $x \in [a,b]$ given $|f'(x)| \leq C|f(x)| $
131876
Show that $\int_{a}^{b}{x^{n}f(x)dx}=0$, then $f=0$
90369
Does $\int_a^bf(x) = 0$ imply $f(x) = 0$ for a Riemann Integral function?
20273
Prove that if $|f(x)| \leq x^2$, then the function is continuous and differentiable at $x=0$.
67364
If $\lim_{x\to\infty}(f(x)+f'(x))=L$ show that $\lim_{x\to\infty} f(x) = L$ and $\lim_{x\to\infty} f'(x) = 0$
155864
Prove or disprove: if $y'=y-y^2$ and $y(0)=a$ where $00$
118266
If $f^2(b) - f^2(a) = b^2 - a^2$, then the equation $f'(x)f(x) = x$ has at least one root in (a, b).
71127
How do I find $f(0)$, $f'(0)$, and $f'(x)$ given $f(x+y)=f(x)+f(y)+x^2y+xy^2$ and $\lim_{x\to0}\frac{f(x)}{x}=1$?
94944
Differentiable functions satisfying $f'(f(x))=f(f'(x))$
17154
Does a non-trivial solution exist for $f'(x)=f(f(x))$?
75390
How does one prove that if function's partial derivative respect to every variable is zero, function is constant?
51659
If $f(0)=0$ then prove that $|f(z)+f(-z)| \leq 2|z|^2$
89537
$ \int_0^x f(t)dt=\int_0^{ax}f(t)dt+ \int_0^{bx}f(t)dt$ implies $f$ constant
76790
Condition to guarantee $f=0$ on $[a,b]$
107727
$m\{x\in [0,1]:f'(x)=0\}>0$