Given $f$ is an even function of interval $(-a, a)$, .... $f'$ is an odd function on $(-a,a)$
15155
Derivative of an even function is odd and vice versa
26219
Suppose f is a function such that f'(x) = 1/x for all x > 0. Prove that if f(1) = 0, then f(xy) = f(x) + f(y) for all x,y > 0
42218
How to find out the following function f which is a function of r?
135693
Suppose f is a twice differentiable function with $f(0)=0$ and $f(1)=1$, $f'(0)=f'(1)=0$. Then show that $|f''(x)| > 4$ for some $x$ in $(0,1)$
24810
Functions satisfying $(b-a)f'(\tfrac{a+b}{2}) = f(b)- f(a)$
82597
How to find $ f(x)$ if $f(1-f(x))=x$ for all $x$ $\in \mathbb{R}$
30204
Prove that $f'(0)$ exists and $f'(0) = b/(a - 1)$
85739
Show that $f(x) = 0$ for all $x \in [a,b]$ given $|f'(x)| \leq C|f(x)| $
83338
Show that there's no continuous function that takes each of its values $f(x)$ exactly twice.
23465
When $f(x+1)-f(x)=f'(x)$, what are the solutions for $f(x)$?
27482
How to show $-\sup(-A)=\inf(A)$?
58013
Integral of Even and Odd functions
115636
Show that $f$ is either injective or a constant function.
68048
Prove that if $f$ is differentiable on $[a,b]$ and $f'$ is monotonic on $[a,b]$ , $f'$ is continuous on $[a,b]$
24466
Prove that if $[F(\alpha):F]$ is odd then $F(\alpha)=F(\alpha^2)$
44880
Prove that the derivative of an even differentiable function is odd, and the derivative of an odd is even.
154288
proof that Even powers of an odd function's taylor polynomial vanish