Let $f(x)$ be a quadratic expression which is positive for all real values of $x.$ If $g(x)=f(x)+f'(x)+f''(x)$
26207
If $f$ is a quadratic and $f(x)>0\;\forall x$, and $g= f + f' + f''$, prove $g(x)>0\; \forall x$
156890
If $f$ and $g$ satisfy the sine/cosine addition formulae, then what is $g'(0)$?
57368
Prove that a positive polynomial function can be written as the squares of two polynomial functions
98255
Find $f(x)$ such that $f(f(x)) = x^2 - 2$
117353
Polynomial equation $f(x)f(2x^2)=f(2x^3+x)$
105999
An application of derivatives problem- to show that $f(x+2)-f(x)>2$ for $f(x)=x\cos(1/x)$
100765
If $f'(x) = 0$ for all $x \in \mathbb{Q}$, is $f$ constant?
111076
If $f$ is non-constant and entire, prove that there exists a $z_0 \in C$ such that $f(z_0)$ is a positive real number
152053
Proof that $\frac{a^2}{b} + \frac{b^2}{c} + \frac{c^2}{a} \geq a+b+c$
133496
is $\sqrt{x}$ always positive?
139111
Prove that $a<c<b$, $\frac{f(b)-f(a)-(b-a)f'(a)}{g(b)-g(a)-(b-a)g'(a)}=\frac{f"(c)}{g"(c)}$
105172
Prove that the entire function is constant over certain conditions.
111756
How do I prove that then $f(x) = 1$ for some $x ∈ [0, 1]$?
138544
For which values of $x$, will $f (x) . f '(x) < 0$?
56818
Prove that if $A$ is positive, then $\exists\;\alpha>0$ such that $\langle Ax, x \rangle\geq \alpha|x|^2$ for $x\in\Bbb{R}^n$
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 $x ≤ 0$.
101918
Let $f(x)=ax^2+bx+c$ where $a,b,c$ are real numbers. Suppose $f(-1),f(0),f(1) \in [-1,1]$. Prove that $|f(x)|\le \frac{3}{2}$ for all $x \in [-1,1]$.