How to show $f(x)$ is $0$ in following problem?
5180
How to show $\alpha\int_a^cf(x)dx+\beta \int_c^b f(x)dx =0$ means $f(x)=0$ everywhere $?$
39921
show that f is constant on I
138544
For which values of $x$, will $f (x) . f '(x) < 0$?
113888
Behavior of derivative near the zero of a function.
61486
Show that $f$ is not differentiable at $(0,0)$ - $\frac{x_1^2x_2}{x_1^2+x_2^2}$
131692
How to show that $f_{0}f_{1}+f_{1}f_{2}+...+f_{2n-1}f_{2n} = f^{2}_{2n}$
16212
If $f$ is continuous, nonnegative on $[a, b]$, show that $\int_{a}^{b} f(x) d(x) = 0$ iff $f(x) = 0$
48314
Show that if a function is not negative and its integral is $0$ than the function is $0$
14994
Showing a function $f$ cannot be surjective
2072
Demonstrate that if $f$ is surjective then $X = f(f^{-1}(X))$
76311
$f'' + f =0$: finding $f$ using power series
74583
Prove that $f'(0)=L$.
156778
Finding functions satisfying $f(f(x))+f(x)+x=0$
86409
Show that $\lim_{x \to +\infty}\left(f(x)+f'(x)\right)=0 \Rightarrow \lim_{x \to +\infty} f(x)=0$
25467
Prove that $\lim f(x) =0$ and $\lim (f(2x)-f(x))/x =0$ imply $\lim f(x)/x =0$
76790
Condition to guarantee $f=0$ on $[a,b]$
11322
Show that $f$ vanishes identically.