Provide an appropriate response.
-Given $f(x, y)=x^{2}+y^{2}$, the purpose of finding the critical points is which of the following?
(i) find local minimums, if they exist
(ii) find local maximums, if they exist
(iii) find saddle points, if they exist
(iv) find interior points, if they exist
A) All are correct.
B) (i), (ii), and (iii) are all correct.
C) Only (i) and (ii) are correct.
D) Only (iii) is correct.

Question

Quizplus · Accepted Answer

The purpose of finding critical points for a function like $f(x, y)=x^{2}+y^{2}$ is to determine where the function has local minimums, local maximums, or saddle points. Critical points are where the gradient is zero or undefined, which can indicate these features. Interior points are not related to critical points.

Provide an Appropriate Response f(x,y)=x2+y2f(x, y)=x^{2}+y^{2}f(x,y)=x2+y2 , the Purpose of Finding the Critical Points Is Which

Provide an Appropriate Response $f(x, y)=x^{2}+y^{2}$ , the Purpose of Finding the Critical Points Is Which