${H_{f(x,y)}} = \left[ \begin{array}{l} {f_{xx}}\,\,\,\,\,{f_{xy}}\,\\ {f_{yx}}\,\,\,\,{f_{yy}} \end{array} \right]$
In the case of $\Delta_2=f_{xx}f_{yy}−(f_{xy})^2<0$, does $(x,y)$ satisfying $f_{xx}f_{yy}>0$ exist?
2026-04-03 01:42:14.1775180534
Partial derevative and saddle point
34 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in CALCULUS
- Equality of Mixed Partial Derivatives - Simple proof is Confusing
- How can I prove that $\int_0^{\frac{\pi}{2}}\frac{\ln(1+\cos(\alpha)\cos(x))}{\cos(x)}dx=\frac{1}{2}\left(\frac{\pi^2}{4}-\alpha^2\right)$?
- Proving the differentiability of the following function of two variables
- If $f ◦f$ is differentiable, then $f ◦f ◦f$ is differentiable
- Calculating the radius of convergence for $\sum _{n=1}^{\infty}\frac{\left(\sqrt{ n^2+n}-\sqrt{n^2+1}\right)^n}{n^2}z^n$
- Number of roots of the e
- What are the functions satisfying $f\left(2\sum_{i=0}^{\infty}\frac{a_i}{3^i}\right)=\sum_{i=0}^{\infty}\frac{a_i}{2^i}$
- Why the derivative of $T(\gamma(s))$ is $T$ if this composition is not a linear transformation?
- How to prove $\frac 10 \notin \mathbb R $
- Proving that: $||x|^{s/2}-|y|^{s/2}|\le 2|x-y|^{s/2}$
Related Questions in MULTIVARIABLE-CALCULUS
- Equality of Mixed Partial Derivatives - Simple proof is Confusing
- $\iint_{S} F.\eta dA$ where $F = [3x^2 , y^2 , 0]$ and $S : r(u,v) = [u,v,2u+3v]$
- Proving the differentiability of the following function of two variables
- optimization with strict inequality of variables
- How to find the unit tangent vector of a curve in R^3
- Prove all tangent plane to the cone $x^2+y^2=z^2$ goes through the origin
- Holding intermediate variables constant in partial derivative chain rule
- Find the directional derivative in the point $p$ in the direction $\vec{pp'}$
- Check if $\phi$ is convex
- Define in which points function is continuous
Related Questions in OPTIMIZATION
- Optimization - If the sum of objective functions are similar, will sum of argmax's be similar
- optimization with strict inequality of variables
- Gradient of Cost Function To Find Matrix Factorization
- Calculation of distance of a point from a curve
- Find all local maxima and minima of $x^2+y^2$ subject to the constraint $x^2+2y=6$. Does $x^2+y^2$ have a global max/min on the same constraint?
- What does it mean to dualize a constraint in the context of Lagrangian relaxation?
- Modified conjugate gradient method to minimise quadratic functional restricted to positive solutions
- Building the model for a Linear Programming Problem
- Maximize the function
- Transform LMI problem into different SDP form
Related Questions in HESSIAN-MATRIX
- Check if $\phi$ is convex
- Gradient and Hessian of quadratic form
- Let $f(x) = x^\top Q \, x$, where $Q \in \mathbb R^{n×n}$ is NOT symmetric. Show that the Hessian is $H_f (x) = Q + Q^\top$
- An example for a stable harmonic map which is not a local minimizer
- Find global minima for multivariable function
- The 2-norm of inverse of a Hessian matrix
- Alternative to finite differences for numerical computation of the Hessian of noisy function
- Interpretation of a Global Minima in $\mathbb{R}^2$
- How to prove that a level set is not a submanifold of dimension 1
- Hessian and metric tensors on riemannian manifolds
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?