From Past Exams 1. (a) Show that $$ f(x, y)=x^{2}+3 y^{2}-2 x y $$ is differentiable on $$ \mathbb{R}^{2} $$. (b) Find all points on the graph of $$ f $$ where the tangent plane is parallel to the plane $$ 2 x+2 y-z=5 $$.

Question

UpStudy AI · Accepted Answer

(أ) الدالة $$ f(x, y) = x^{2} + 3y^{2} - 2xy $$ قابلة للاشتقاق على $$ \mathbb{R}^{2} $$ لأن مشتقاتها الجزئية مستمرة. (ب) النقاط التي تجعل المستوى المماس للدالة موازياً للمستوى $$ 2x + 2y - z = 5 $$ هي $$ (2y, y, 3y^{2}) $$ حيث $$ y $$ هو أي عدد حقيقي.

From Past Exams 1. (a) Show that \( f(x, y)=x^{2}+3 y^{2}-2 x y \) is differentiable on \( \mathbb{R}^{2} \). (b) Find all points on the graph of \( f \) where the tangent plane is parallel to the plane \( 2 x+2 y-z=5 \).

UpStudy ThothAI Solution

Quick Answer

Step-by-step Solution

From Past Exams 1. (a) Show that \( f(x, y)=x^{2}+3 y^{2}-2 x y \) is differentiable on \( \mathbb{R}^{2} \). (b) Find all points on the graph of \( f \) where the tangent plane is parallel to the plane \( 2 x+2 y-z=5 \).

UpStudy ThothAI Solution

Quick Answer

Step-by-step Solution

Related Questions