Page |1
UTA Math 2326 Exam 2 Questions and
Correct Answers/ Latest Update / Already
Graded
What is the procedure for locating absolute maximum and minimum
values on a closed bounded domain R?
Ans: Determine the values of the function at all critical points
in R. Then find the maximum and minimum values on the
boundary of R. The greatest of these values is the absolute
maximum on R, and the least of these is the absolute minimum.
How to numerically find the critical points of function f(x,y)
Ans: You take fx(x,y) and fy(x,y) and set them to 0 to find what
x and y needs for that to work
How to find if there is a local maximum, local minimum, or saddle point
and what that point is.
Ans: Find D(x,y)=fxx(x,y)fyy(x,y) - (fxy(x,y))^2 at the critical
point (a,b)
if D(a,b)>0 and fxx(a,b)<0 then there is a local max at (a,b)
if D(a,b)>0 and fxx(a,b)>0 then there is a local minimum at (a,b)
if D(a,b)<0 then f has a saddle point at (a,b)
if D(a,b)=0 then the result is inconclusive
All rights reserved © 2025/ 2026 |
, Page |2
How to find minimums, maximums, and saddle points when D(x,y)=0
Ans: Find f(x,y) at the critical point(s)
D(x,y,z)
Ans: d(x,y,z)^2=(x-a)^2+(y-b)^2+(z-c)^2
How to find the absolute maximum and minimum using lagrange
multipliers, With formulas f(x,y) and g(x,y)
Ans: set VF = λVG
Find λ and plug it into the other equation
Find the value of X and Y
plug into g(x) to find the value of x/y
Plug all coordinates into f(x), biggest values are maximum,
smallest are the minimums
How to find a point on a plane x + y + z + d = 0 closest to the point
(a,b,c)
Ans: set f(x,y,z) = D(x,y,z)^2 and use the plane as g(x) then find
the maximum
All rights reserved © 2025/ 2026 |
UTA Math 2326 Exam 2 Questions and
Correct Answers/ Latest Update / Already
Graded
What is the procedure for locating absolute maximum and minimum
values on a closed bounded domain R?
Ans: Determine the values of the function at all critical points
in R. Then find the maximum and minimum values on the
boundary of R. The greatest of these values is the absolute
maximum on R, and the least of these is the absolute minimum.
How to numerically find the critical points of function f(x,y)
Ans: You take fx(x,y) and fy(x,y) and set them to 0 to find what
x and y needs for that to work
How to find if there is a local maximum, local minimum, or saddle point
and what that point is.
Ans: Find D(x,y)=fxx(x,y)fyy(x,y) - (fxy(x,y))^2 at the critical
point (a,b)
if D(a,b)>0 and fxx(a,b)<0 then there is a local max at (a,b)
if D(a,b)>0 and fxx(a,b)>0 then there is a local minimum at (a,b)
if D(a,b)<0 then f has a saddle point at (a,b)
if D(a,b)=0 then the result is inconclusive
All rights reserved © 2025/ 2026 |
, Page |2
How to find minimums, maximums, and saddle points when D(x,y)=0
Ans: Find f(x,y) at the critical point(s)
D(x,y,z)
Ans: d(x,y,z)^2=(x-a)^2+(y-b)^2+(z-c)^2
How to find the absolute maximum and minimum using lagrange
multipliers, With formulas f(x,y) and g(x,y)
Ans: set VF = λVG
Find λ and plug it into the other equation
Find the value of X and Y
plug into g(x) to find the value of x/y
Plug all coordinates into f(x), biggest values are maximum,
smallest are the minimums
How to find a point on a plane x + y + z + d = 0 closest to the point
(a,b,c)
Ans: set f(x,y,z) = D(x,y,z)^2 and use the plane as g(x) then find
the maximum
All rights reserved © 2025/ 2026 |
