query: A problem on conituous first derivative function
positive_passages.docid: 144439
positive_passages.text: For a $C^1$ function, the difference $|{g'(c)} - {{g(d)-g(c)} \over {d-c}} |$ is small when $|d-c|$ is small
negative_passages.docid: 75548
negative_passages.text: second derivative of the inverse function
negative_passages.docid: 105293
negative_passages.text: Proof of the second symmetric derivative
negative_passages.docid: 75390
negative_passages.text: How does one prove that if function's partial derivative respect to every variable is zero, function is constant?
negative_passages.docid: 45363
negative_passages.text: Show that both mixed partial derivatives exist at the origin but are not equal
negative_passages.docid: 96022
negative_passages.text: Symmetry of second derivative - Sufficiency of twice-differentiability
negative_passages.docid: 117338
negative_passages.text: Counterexample to second derivative test when f''(x) is not continuously differentiable
negative_passages.docid: 39995
negative_passages.text: Showing that partial derivatives of $f(x) = \frac{xy}{x^2+y^2}$ exist for $(x,y) \neq (0,0)$
negative_passages.docid: 125774
negative_passages.text: Derivative of $a^x$ from first principles
negative_passages.docid: 4735
negative_passages.text: Proof for alternative definition of the derivative
negative_passages.docid: 37303
negative_passages.text: Differential of a smooth function
negative_passages.docid: 129324
negative_passages.text: Let $f:[0;1]\to\mathbb R$ be continiously differentiable
negative_passages.docid: 77624
negative_passages.text: Characterization of sets of differentiability
negative_passages.docid: 111470
negative_passages.text: Proof of differentiability of $f(x)$
negative_passages.docid: 150833
negative_passages.text: Discontinuities of the derivative of a differentiable function on closed interval
negative_passages.docid: 131444
negative_passages.text: Local maximum implies derivative is $0$
negative_passages.docid: 105319
negative_passages.text: A calculus problem with functions such that $f''(x) = g(x)$ and $g''(x) = f(x)$