Let f be twice continuously differentiable on [a, b] and f(a)=f(b)=0
133990
How prove this $\int_{a}^{b}f(x)dx=\frac{1}{2}(b-a)[f(a)+f(b)]-\frac{1}{12}(b-a)^3f''(\xi)$
132013
How do I show that if $f : [0,1] \to [0,1]$ is continuous, then there is some $c$ such that $f(c) = c$?
34136
$f$ is differentiable in $[0,1]$ ,$\sup_{x\in[0,1]}|f'(x)| \le M\lt+\infty $
9270
Differentiable function, with $f'(x)=[f(x)]^2$
2506
twice differentiable functions
130748
Infinitely differentiable function with given zero set?
80650
Complex differentiability of $f(z)=|z|$
150554
proof that $f'$ is continuous at $a$
119042
If $f+g$ and $f$ are differentiable at $a$, must $g$ be differentiable at $a$?
145919
If $f: \Bbb{R}\rightarrow\Bbb{R}$ is continuous at $0$ and $f(x)=f(2x)$ for each $x\in\Bbb{R}$ then $f$ is constant.
12498
Derivable function on an interval $ [a,b]$ with derivative unbounded on $[a,b]$
75735
Let $f$ be a continuous function on an interval around $0$ and let $a_i=f(\frac{1}{i})$ (for large enough $i$)
152328
A continuously differentiable map is locally Lipschitz
105700
Proving $\,f$ is constant.
88311
Linear functional f(v)=0 imply v=0
42900
Locally continuously differentiable implies locally Lipschitz
16212
If $f$ is continuous, nonnegative on $[a, b]$, show that $\int_{a}^{b} f(x) d(x) = 0$ iff $f(x) = 0$