Locate-the-critical-points-of-the-following-functions-and-state-the-nature-of-each-1-f-x-y-3x-4-2x-2-2xy-x-3y-2-6y-15-2-f-x-y-x-2-4xy-y-2-

Tinku Tara June 3, 2023 Vector Calculus 0 Comments

Question Number 135933 by Engr_Jidda last updated on 17/Mar/21

Locate the critical points of the following functions and state the nature of each. (1) f(x,y)=3x^4 −2x^2 +2xy−x+3y^2 −6y+15 (2) f(x,y)=x^2 −4xy+y^2

$${Locate}\:{the}\:{critical}\:{points}\:{of}\:{the}\:{following} \\ $$$${functions}\:{and}\:{state}\:{the}\:{nature}\:{of}\:{each}. \\ $$$$\left(\mathrm{1}\right)\:{f}\left({x},{y}\right)=\mathrm{3}{x}^{\mathrm{4}} −\mathrm{2}{x}^{\mathrm{2}} +\mathrm{2}{xy}−{x}+\mathrm{3}{y}^{\mathrm{2}} −\mathrm{6}{y}+\mathrm{15} \\ $$$$\left(\mathrm{2}\right)\:{f}\left({x},{y}\right)={x}^{\mathrm{2}} −\mathrm{4}{xy}+{y}^{\mathrm{2}} \\ $$

Answered by dhgt last updated on 04/May/21