Let $f$ be a differentiable function with $|f'(x)|\leq1$ and $f(-3)=-3, f(3)=3$. Then find $f(0)$.
118565
Find a function value given 2 points
28949
Prove $f(x) = 0 $for all $x \in [0, \infty)$ when $|f'(x)| \leq |f(x)|$
113343
$f$ is constant if derivative equals zero
151819
A twice differentiable function $f$ satisfies $f′′(x)+f(x)=−xg(x)f′(x)$, $\forall x\ge 0$.
23465
When $f(x+1)-f(x)=f'(x)$, what are the solutions for $f(x)$?
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 $\lim_{x\to0}\frac{f(x)}{x}=1$?
52858
Find $f$ if $ f(x)+f\left(\frac{1}{1-x}\right)=x $
109561
Find $F'(x)$ if $F(x) = \displaystyle \int_{0}^x xf(t)dt$.
144773
function $f(x)=x^{-(1/3)}$ , please check whether my solution is correct?
38417
How to find the non-differentiable point(s) of a given continuous function?
142682
Find $f(x)$ where $ f(x)+f\left(\frac{1-x}x\right)=x$
85480
Let $f(x,y)=\frac{x^3-y^3}{x^2+y^2}$. Is f differentiable in $(0,0)$?
103706
If $\{f(0)\}^{2} + \{f'(0)\}^{2} = 4$ then there is a $c$ with $f(c) + f''(c) = 0$
8854
Prove $f $ is identically zero if $f(0)=0$ and $|f'(x)|\le|f(x)|$
122407
If $f(x) = x^3+3x+4\;,$ Then value of $ \int_{-1}^{1}f(x)dx+\int_{0}^{4}f^{-1}(x)dx$
16375
Is the function differentiable at $0$?
138544
For which values of $x$, will $f (x) . f '(x) < 0$?