proof $[f(b)-f(a)]g'(c) = [g(b)-g(a)]f'(c)$
77645
Generalized mean value theorem
62270
Given two increasing continuous functions $f,g$ prove that $(b-a) \int^b_a f(x)g(x) dx > \int^b_a f(x) dx \int^b_a g(x) dx$
110313
Prove that $\gcd(f(x),g(x)) = 1$.
7858
Proving that $f(x)$ is irreducible over $F(b)$ if and only if $g(x)$ is irreducible over $F(a)$
144589
Proving that if $f(x) \le g(x)$ then $f(x_0) \le g(x_0)$
39090
Finding functions such that $f(g(x)) = f(x)g(x)$
85612
Let functions $ f: A \to B$ and $g: B \to A$, suppose that $ g \circ f = i_A$. Prove that if $f$ is onto, then $g$ is one-to-one
94571
How can we prove that $N_G(H)=H$ implies $N_{f(G)}(f(H))=f(H)$
82935
Prove that f∈Θ(g)if and only ifO(f) =O(g).
34081
Prove that $|f''(\xi)|\geqslant\frac{4|f(a)-f(b)|}{(b-a)^2}$
43733
$|f'(x)| \le g(x)$ implies $|f(b) - f(a)| \le \int_a^b g(x) dx$, without assuming $f'$ to be integrable.
70128
Prove that $(fg)^{(n)} = \sum_{k=0}^n \binom{n}{k}f^{(k)}(x)g^{(n-k)}(x)$
30204
Prove that $f'(0)$ exists and $f'(0) = b/(a - 1)$
126989
Prove that $g(z)=\overline{f(z)}$ is complex diﬀerentiable at $a$ if and only if $f'(a) = 0$.
33196
show that A(T) is a group under operation of composition of functions
120960
$f,g$ such that $\int fg = \int f \int g$
26207
If $f$ is a quadratic and $f(x)>0\;\forall x$, and $g= f + f' + f''$, prove $g(x)>0\; \forall x$