Prove that $f(x) = 0$ for all $x ∈ R$.
69869
if $f$ is continuous on $\mathbb{R}$ and $f(r)=0,r \in \mathbb{Q}$, then $f(x)=0,x \in \mathbb{R}$
18261
Prove $\int_{a}^{b}{f(x)dx}>0$.
57193
Prove that $f$ has derivatives of all orders at $x=0$, and that $f^{(n)}(0)=0$ for $n=1,2,3\ldots$
4636
How to show that $f$ is differentiable at $x=0.$
57026
$f(0)=f'(0)=f'(1)=0$ and $f(1)=1$ implies $\max|f''|\geq 4$
107727
$m\{x\in [0,1]:f'(x)=0\}>0$
76148
Show that $\exists c \in \mathbb{R} : f(c) = 0$
71225
$f(0)=0$ and $\lim_{x \to \infty}f(x)=0$. Show there's $x_0$ such that $f'(x_0)=0$
91388
Prove that $f$ is a polynomial if one of the coefficients in its Taylor expansion is 0
112323
Showing that $f = 0 $ a.e. if for any measurable set $E$, $\int_E f = 0$
69707
If $f(x + y) \leq yf(x) + f(f(x))$ for all real numbers $x$ and $y$, then prove that $f(x) = 0$ for all $x ≤ 0$.
136980
Prove there exists $a\in \Bbb{R}$ such that $f'(a)=0$.
13202
Prove that there exists at least one $x_0\in\mathbb{R}$, such that $f(x_0)+f''(x_0)=0$
95469
Suppose $f:[0,1] \Rightarrow \mathbb{R}$ is continuous and $\int_0^x f(x)dx = \int_x^1 f(x)dx$. Prove that $f(x) = 0$ for all $x$
148813
Prove: $f: \mathbb{R} \rightarrow \mathbb{R}$ st for every $x \in \mathbb{R}$ there exists $n$ st $f^{(n)}(x) = 0$, f is a polynomial.
140988
Prove $\exp(x)\exp(y)=\exp(y)\exp(x)$ if $[x,y]=0$.
75390
How does one prove that if function's partial derivative respect to every variable is zero, function is constant?