query: Continuous $f:[0,1]\to\mathbb{R}$ is differentiable on $(0,1]$ and $\lim_{x\to 0^+} f'(x)$ is finite. Prove that f has right hand derivative at x=0
positive_passages.docid: 1371
positive_passages.text: Prove that $f'(a)=\lim_{x\rightarrow a}f'(x)$.
negative_passages.docid: 97104
negative_passages.text: Proof that continuous function on $ [0, 2]$ has $f(x) = f(x-1)$ for some $ x$
negative_passages.docid: 3387
negative_passages.text: Derivative of $f(x)=|x|$
negative_passages.docid: 68048
negative_passages.text: Prove that if $f$ is differentiable on $[a,b]$ and $f'$ is monotonic on $[a,b]$ , $f'$ is continuous on $[a,b]$
negative_passages.docid: 150554
negative_passages.text: proof that $f'$ is continuous at $a$
negative_passages.docid: 132013
negative_passages.text: How do I show that if $f : [0,1] \to [0,1]$ is continuous, then there is some $c$ such that $f(c) = c$?
negative_passages.docid: 29582
negative_passages.text: Continuous mapping $f: [0,1]\rightarrow (0,1)$ CSIR December $2013$
negative_passages.docid: 53627
negative_passages.text: Proving continuity of $f$
negative_passages.docid: 115635
negative_passages.text: Differentiability of antiderivative and continuity of derivative
negative_passages.docid: 143874
negative_passages.text: Limit of derivative is zero. Does it imply a limit for f(x)?
negative_passages.docid: 76908
negative_passages.text: If $f'$ is differentiable at $a$ then $f'$ is continuous at $(a-\delta,a+\delta)$
negative_passages.docid: 108593
negative_passages.text: First order weak derivatives of $f(x)=|x|^r$
negative_passages.docid: 30455
negative_passages.text: Show that any continuous $f:[0,1] \rightarrow [0,1]$ has a fixed point $\zeta$
negative_passages.docid: 133405
negative_passages.text: $\lim_{x \rightarrow 0} f'(x) = L$ exists, does it follow that $f'(0)$ exists?
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: 97256
negative_passages.text: For $f$ continuous, show $\lim_{n\to\infty} n\int_0^1 f(x)x^n\,dx = f(1).$
negative_passages.docid: 96450
negative_passages.text: If $f(x)$ is continuous and differentiable function , prove that $f(x) \geq e^{3x}, \forall x \geq 0$