If $(x-a)^2|f(x)$, then $(x-a)|f'(x)$ and if $(x-a)|f(x)$ and $(x-a)|f'(x)$, then $(x-a)^2|f(x)$
45811
How to prove that r is a double root if and only if it is a root of a polynomial and of its derivative.
45602
Show that is $\int_A f$ exists, then so does $\int_A |f|$
9270
Differentiable function, with $f'(x)=[f(x)]^2$
1641
Proving $f' = - \frac{\partial{F}/\partial{x}}{\partial{F}/\partial{y}}$
72694
Proving that $f(x) = g(x)$ for some $x \in [a,b]$ if $f,g$ continuous, $f(a)  g(b)$
74100
How do you solve $f'(x) = f(f(x))$?
35889
Suppose that f(0) = f(1) = 0 and x ∈ (0, 1). Prove that there exists c ∈ (0, 1) such that f'(c) = f(x).
105999
An application of derivatives problem- to show that $f(x+2)-f(x)>2$ for $f(x)=x\cos(1/x)$
409
functions satisfying $f(x - y) = f(x) f(y) - f(a - x) f(a + y)$ and $f(0)=1$
68746
What is $f(f^{-1}(A))$?
98255
Find $f(x)$ such that $f(f(x)) = x^2 - 2$
58943
If $f'(x)\le g'(x)$, prove $f(x)\le g(x)$
106748
Number of functions $f : A \to A$ such that $f(f(x))=f(x)$
132971
Prove that $|a| < b \iff -b<a<b$
17310
Can $f(x)=|x|^3$ be differentiated
36697
Proving that $\int_{-b}^{-a}f(-x)dx=\int_{a}^{b}f(x)dx$
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 $x \in [-1,1]$.