query: A function on [a,b] that is second differentiable and f'(a)=f'(b)=0
positive_passages.docid: 34081
positive_passages.text: Prove that $|f''(\xi)|\geqslant\frac{4|f(a)-f(b)|}{(b-a)^2}$
negative_passages.docid: 17343
negative_passages.text: Function on $[a,b]$ that satisfies a Hölder condition of order $\alpha > 1 $ is constant
negative_passages.docid: 111470
negative_passages.text: Proof of differentiability of $f(x)$
negative_passages.docid: 129716
negative_passages.text: Let $f$ be continuous on $ [a,b]$, differentiable on $ (a,b) $ and $ f(x) \neq 0 \forall x \in (a,b) $ Prove $ \exists c \in (a,b) $ such that
negative_passages.docid: 127390
negative_passages.text: Second derivative of a composite function
negative_passages.docid: 143491
negative_passages.text: Show that $f$ is differentiable on $(−1, 1)$.
negative_passages.docid: 53497
negative_passages.text: Prove that the function is continuous and differentiable (not as easy as it sounds imo)
negative_passages.docid: 30204
negative_passages.text: Prove that $f'(0)$ exists and $f'(0) = b/(a - 1)$
negative_passages.docid: 150833
negative_passages.text: Discontinuities of the derivative of a differentiable function on closed interval
negative_passages.docid: 77331
negative_passages.text: $f$ function with $\nabla f=\bar{0}$
negative_passages.docid: 112923
negative_passages.text: Let $f:\mathbb{R}\longrightarrow \mathbb{R}$ a differentiable function such that $f'(x)=0$ for all $x\in\mathbb{Q}$
negative_passages.docid: 138864
negative_passages.text: If $f\colon \mathbb{R} \to \mathbb{R}$ is such that $f(x+y)=f(x)f(y)$ and $f'(0)$ exists, then $f$ is differentiable on $\mathbb R$
negative_passages.docid: 131357
negative_passages.text: Prove that $f(x,y)=xy$ is differentiable using the definition
negative_passages.docid: 74810
negative_passages.text: A function $f$ such that $f' = 0$ when $x < 0$ and $f' = 1$ when $x \geq 0$?
negative_passages.docid: 34136
negative_passages.text: $f$ is differentiable in $[0,1]$ ,$\sup_{x\in[0,1]}|f'(x)| \le M\lt+\infty $
negative_passages.docid: 83915
negative_passages.text: Showing that a function is not differentiable
negative_passages.docid: 151958
negative_passages.text: How to show $f'(0)$ exist and is equal to $1$?