Prove that $g'' = f$
65889
Showing $\Phi(x)=\int_0^x (x-t)f(t)\,dt$ is twice differentiable and finding $\Phi''(x)$
130537
Proving that $d(f,g)=\|f-g\| = \sup \limits_{0\leq x \leq 1} |f(x)-g(x)|$ is a metric on $X=C[0,1]$
139111
Prove that $a<c<b$, $\frac{f(b)-f(a)-(b-a)f'(a)}{g(b)-g(a)-(b-a)g'(a)}=\frac{f"(c)}{g"(c)}$
10431
Prove that $C\exp(x)$ is the only set of functions for which $f(x) = f'(x)$
145424
If $f''(x)+f(x)>0$ and $f(x)>0$ $\forall x\in(a,b)$; $f(a)=f(b)=0$; prove that $b-a>\pi$.
48592
Prove that $f'$ exists for all $x$ in $R$ if $f(x+y)=f(x)f(y)$ and $f'(0)$ exists
105068
Proving that the function is differentiable and $f'(0)=0$
43733
$|f'(x)| \le g(x)$ implies $|f(b) - f(a)| \le \int_a^b g(x) dx$, without assuming $f'$ to be integrable.
147299
Prove that $g(x,y) = \frac{x^3y}{x^2+y^2}$ with $g(0,0)=0$ is continuous
21879
Show that if $\lim_{x\to a}f'(x) = A$ then $f'(a)$ exists and equals A
58832
How prove this $\int_{a}^{b}[f''(x)]^2dx\ge\dfrac{4}{b-a}$
69008
$f'(x) = [f(x)]^{2}$. Prove $f(x) = 0 $
111186
Proving that if $|f''(x)| \le A$ then $|f'(x)| \le A/2$
144589
Proving that if $f(x) \le g(x)$ then $f(x_0) \le g(x_0)$
43956
Differentiating $f(x)^{g(x)}$
154001
$(g\circ f)^{-1}=f^{-1}\circ g^{-1}$
104949
How would I prove that this function is affine if $f(x+h)-f(x)=hf'(x)$?