$f(0)^2+f'(0)^2=4$ then $f(x_0)+f''(x_0)=0$
103706
If $\{f(0)\}^{2} + \{f'(0)\}^{2} = 4$ then there is a $c$ with $f(c) + f''(c) = 0$
112923
Let $f:\mathbb{R}\longrightarrow \mathbb{R}$ a differentiable function such that $f'(x)=0$ for all $x\in\mathbb{Q}$
76311
$f'' + f =0$: finding $f$ using power series
156778
Finding functions satisfying $f(f(x))+f(x)+x=0$
63750
let $f(\frac{x}{3})+f(\frac{2}{x})=\frac{4}{x^2}+\frac{x^2}{9}-2$ then find $f(x)$
64339
Find $f$ where $f'(x) = f(1+x)$
57026
$f(0)=f'(0)=f'(1)=0$ and $f(1)=1$ implies $\max|f''|\geq 4$
51659
If $f(0)=0$ then prove that $|f(z)+f(-z)| \leq 2|z|^2$
35889
Suppose that f(0) = f(1) = 0 and x ∈ (0, 1). Prove that there exists c ∈ (0, 1) such that f'(c) = f(x).
71225
$f(0)=0$ and $\lim_{x \to \infty}f(x)=0$. Show there's $x_0$ such that $f'(x_0)=0$
4636
How to show that $f$ is differentiable at $x=0.$
36358
How prove that $\lim\limits_{x\to+\infty}f(x)=\lim\limits_{x\to+\infty}f'(x)=0$ if $\lim\limits_{x\to+\infty}([f'(x)]^2+f^3(x))=0$?
121771
Proof $f(x)\equiv 0$
30204
Prove that $f'(0)$ exists and $f'(0) = b/(a - 1)$
27809
Find the function equation $f(x+f(y)+yf(x))=y+f(x)+xf(y)$
67364
If $\lim_{x\to\infty}(f(x)+f'(x))=L$ show that $\lim_{x\to\infty} f(x) = L$ and $\lim_{x\to\infty} f'(x) = 0$
132093
Solve $f(f(x))=f(x)$