Prove positivity of $f$ when $f'' > f$
107795
If $\,f''(x) \ge f(x)$, for all $x\in[0,\infty),$ and $\,f(0)=f'(0)=1$, then is $\,f(x)>0$?
105268
prove inequality through mean value theorem
120676
A certain element which makes functionals positive
111756
How do I prove that then $f(x) = 1$ for some $x ∈ [0, 1]$?
129579
If $f''(x_0)$ exists then $\lim_{x \to x_0} \frac{f(x_0+h)-2f(x_0)+f(x_0-h)}{h^2} = f''(x_0)$
21301
If nonnegative $f: [0,1] \rightarrow \mathbb{R}$ has a continuous $f''$, then $\int_0^1 \Big| \frac{f''(x)}{f(x)} \Big| \,dx >4$
101778
Show that there is $\eta\in(0,1)$ with $f''(\eta)=f(\eta)$
1371
Prove that $f'(a)=\lim_{x\rightarrow a}f'(x)$.
108115
If $f: [0,1]\rightarrow \mathbb{R}$ is continuous function positive
75137
proving that $f(x) = x^s$ is holder continuous with holder exponent s
145424
If $f''(x)+f(x)>0$ and $f(x)>0$ $\forall x\in(a,b)$; $f(a)=f(b)=0$; prove that $b-a>\pi$.
149739
Prove: $f(t)\leq t+1$
111470
Proof of differentiability of $f(x)$
133682
Prove that if $f(t)$ satisfies $f(t)=f'(t)$, then $f(t+s)=f(t)f(s)$ for all $t,s\in R$ without using the fact that $f(t)=c\cdot e^t$.
21879
Show that if $\lim_{x\to a}f'(x) = A$ then $f'(a)$ exists and equals A
8913
Show that there is $\xi$ s.t. $f(\xi)=f\left(\xi+\frac{1}{n}\right)$
14578
Proving that an additive function $f$ is continuous if it is continuous at a single point