query: Proving existence of points in a twice differentiable function
positive_passages.docid: 150005
positive_passages.text: Existence of points in a differentiable function
negative_passages.docid: 135693
negative_passages.text: 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 $(0,1)$
negative_passages.docid: 8226
negative_passages.text: Proving that a function has a removable singularity at infinity
negative_passages.docid: 111470
negative_passages.text: Proof of differentiability of $f(x)$
negative_passages.docid: 142490
negative_passages.text: Alternative proof for differentiability of inverse function?
negative_passages.docid: 31522
negative_passages.text: Proving $f$ has at least one zero inside unit disk
negative_passages.docid: 90435
negative_passages.text: Prove that there exist linear functionals $L_1, L_2$ on $X$
negative_passages.docid: 137527
negative_passages.text: if $f(x)$ is differentiable at a x, prove that: $\lim_{h\to0}\frac{f(x+h)-f(x-h)}{2h}$
negative_passages.docid: 129324
negative_passages.text: Let $f:[0;1]\to\mathbb R$ be continiously differentiable
negative_passages.docid: 26955
negative_passages.text: Continuous at exactly two points and differentiable at exactly one of them
negative_passages.docid: 90970
negative_passages.text: How to prove the line exist?
negative_passages.docid: 111458
negative_passages.text: Prove that $f$ is differentiable
negative_passages.docid: 30330
negative_passages.text: How can I prove that this function is bounded using the given 2 hints?
negative_passages.docid: 150373
negative_passages.text: Number of Fixed Point(s) of a Differentiable Function
negative_passages.docid: 3818
negative_passages.text: Proving two entire functions are constant.
negative_passages.docid: 13202
negative_passages.text: Prove that there exists at least one $x_0\in\mathbb{R}$, such that $f(x_0)+f''(x_0)=0$
negative_passages.docid: 30204
negative_passages.text: Prove that $f'(0)$ exists and $f'(0) = b/(a - 1)$