Prove $\exists \xi \in (-2,2):f(\xi)+f''(\xi)=0.$
13202
Prove that there exists at least one $x_0\in\mathbb{R}$, such that $f(x_0)+f''(x_0)=0$
149764
If $f$ s twice differentiable and satisfies the following constraints, prove $f'(0)>-\sqrt 2$
98344
Prove that $\int_0^1[f''(x)]^2dx\ge4.$
17154
Does a non-trivial solution exist for $f'(x)=f(f(x))$?
71225
$f(0)=0$ and $\lim_{x \to \infty}f(x)=0$. Show there's $x_0$ such that $f'(x_0)=0$
78834
if f(x) if differentiable and continuous, prove $\frac{af(a)-bf(b)}{a-b} = f(c) + cf'(c) $
64485
Proving $\displaystyle\lim_{h\to0}\frac{f(x+h)-2f(x)+f(x-h)}{h^2}=f''(x)$
151805
Prove that $\tau (x_1 x_2 ... x_k) \tau^{-1} = (\tau(x_1) \tau(x_2) ... \tau (x_k))$
40564
Prove that $u(x,t)=\int_{-\infty}^{\infty}c(w)e^{-iwx}e^{-kw^2t}dw\rightarrow 0$ if $x\rightarrow \infty$
1641
Proving $f' = - \frac{\partial{F}/\partial{x}}{\partial{F}/\partial{y}}$
26219
Suppose f is a function such that f'(x) = 1/x for all x > 0. Prove that if f(1) = 0, then f(xy) = f(x) + f(y) for all x,y > 0
76148
Show that $\exists c \in \mathbb{R} : f(c) = 0$
105769
Prove that $\exists a, b\in(0,1)$ such that $\int_0^{a} xf(x)dx=0\text{ and }\int_0^bxf(x)dx=\frac{b^2f(b)}{2}.$
40549
How to proof the the derivative of $x^2$ is $2x$?
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 $x_{0} = 0$ `
51659
If $f(0)=0$ then prove that $|f(z)+f(-z)| \leq 2|z|^2$
82567
Prove that $ f(x) $ has at least two real roots in $ (0,\pi) $