query: How to prove that $f$ is differentiable at every point beside $x=-1$?
positive_passages.docid: 27888
positive_passages.text: Why is $|x|$ not differentiable at $x=0$?
negative_passages.docid: 13150
negative_passages.text: If the derivative of $f$ is never zero, then $f$ is one-to-one
negative_passages.docid: 113888
negative_passages.text: Behavior of derivative near the zero of a function.
negative_passages.docid: 44129
negative_passages.text: If $f:\mathbb{R}\rightarrow \mathbb{R}$ is differentiable and $\lim_{x\to \infty } f^\prime(x)=0$ show that $\lim _{x\to \infty } (f(x+1)-f(x))=0$.
negative_passages.docid: 115712
negative_passages.text: Application of Derivatives rigorous proof
negative_passages.docid: 78834
negative_passages.text: if f(x) if differentiable and continuous, prove $\frac{af(a)-bf(b)}{a-b} = f(c) + cf'(c) $
negative_passages.docid: 83915
negative_passages.text: Showing that a function is not differentiable
negative_passages.docid: 28399
negative_passages.text: Showing $f$ is constant
negative_passages.docid: 127114
negative_passages.text: Differentiability implying continuity
negative_passages.docid: 38417
negative_passages.text: How to find the non-differentiable point(s) of a given continuous function?
negative_passages.docid: 131357
negative_passages.text: Prove that $f(x,y)=xy$ is differentiable using the definition
negative_passages.docid: 105084
negative_passages.text: Let f be a function twice differentiable and with derivatives continuous on an interval $[a,b]$ containing $0$. Prove the following statement:
negative_passages.docid: 129324
negative_passages.text: Let $f:[0;1]\to\mathbb R$ be continiously differentiable
negative_passages.docid: 93712
negative_passages.text: Let $f:(-1,1) \rightarrow \mathbb{R}$ be smooth on $(-1,1)$, $f(0) = 1$. Find $f(x)$.
negative_passages.docid: 2072
negative_passages.text: Demonstrate that if $f$ is surjective then $X = f(f^{-1}(X))$
negative_passages.docid: 105068
negative_passages.text: Proving that the function is differentiable and $f'(0)=0$
negative_passages.docid: 53767
negative_passages.text: How to prove that derivatives have the Intermediate Value Property