Engineering Math Practice Test: Maxima and Minima | Practice Test / Quiz / MCQs

Classes | Practice Tests / Quizzes | User Guide | Life Manuals

28.5K quizzes covering K–12, CBSE, SAT, ACT, GRE, UPSC, SSC, Banking, Reasoning & more.

Engineering Mathematics
| Take A Quiz

Home > Engineering Mathematics > Quizzes > Engineering Math Practice Test: Maxima and Minima

Engineering Math Practice Test: Maxima and Minima

Fast practice, instant feedback. Timer auto-submits when time’s up.

Avg score: 0% • Most missed: “Among the following which is the correct expression for Taylor’s theorem in two …”

Maxima and Minima topics include: Maxima and minima of variables, taylors theorem two variables, lagrange method to find maxima or minima. Maxima and minima are the largest and smallest values taken by a function. They are also known as extrema, which means "an extreme value" within a given range or domain of a function. Maxima are points where a function reaches its highest value, while minima are points where it reaches its lowest value. Local maxima/minima are relative extremes within a specific region, while global maxima/minima are the overall highest and lowest points across the... Show more

Maxima and Minima topics include: Maxima and minima of variables, taylors theorem two variables, lagrange method to find maxima or minima.

Maxima and minima are the largest and smallest values taken by a function. They are also known as extrema, which means "an extreme value" within a given range or domain of a function.

Maxima are points where a function reaches its highest value, while minima are points where it reaches its lowest value.

Local maxima/minima are relative extremes within a specific region, while global maxima/minima are the overall highest and lowest points across the entire domain.

To find the maxima and minimum of a function, you should solve the equation of the derivative equated to zero.

Show less

Engineering Math Practice Test: Maxima and Minima

Time left 00:00

1. Stationary point is a point where, function f(x,y) have?

∂f⁄∂x = 0∂f⁄∂x = 0 & ∂f⁄∂y = 0∂f⁄∂y = 0∂f⁄∂x < 0 and ∂f⁄∂y > 0

2. Which one of these is the right formula for the Lagrange multiplier with more than one constraint?

∇f = μ * ∇g1 + λ * ∇g2∇f = μ * ∇g1 + ∇g2∇f = (μ)2 * ∇g1 + ∇g2Cannot be applied to more than one constraint function.

3. Expansion of \(f (x,y) = tan^{-1} \frac{⁡y}{x}\) upto first degree containing (x+1) & (y-1) is __________

\(\frac{5π}{4} + \frac{(x+1)}{1!} \frac{-1}{2} + \frac{(y-1)}{1!} \frac{-1}{2} + \frac{(x+1)^2}{2!} \frac{-1}{4} + \frac{(y-1)^2}{2!} \frac{1}{4}\) \(\frac{3π}{4} + \frac{(x+1)}{1!} \frac{-1}{2} + \frac{(y-1)}{1!} \frac{-1}{2} + \frac{(x+1)^2}{2!} \frac{-1}{2} + \frac{(y-1)^2}{2!} \frac{1}{2}\) \(\frac{π}{4} + \frac{(x+1)}{1!} \frac{-1}{2} + \frac{(y-1)}{1!} \frac{-1}{2} + \frac{(x+1)^2}{2!} \frac{1}{4} + \frac{(y-1)^2}{2!} \frac{1}{4}\) \(\frac{3π}{4} + \frac{(x+1)}{1!} \frac{-1}{2} + \frac{(y-1)}{1!} \frac{-1}{2} + \frac{(x+1)^2}{2!} \frac{-1}{4} + \frac{(y-1)^2}{2!} \frac{1}{4}\)

4. In a simple one-constraint Lagrange multiplier setup, the constraint has to be always one dimension lesser than the objective function.

FalseMaybeTrueDon't Know

5. Discuss maximum or minimum value of f(x,y) = y² + 4xy + 3x² + x³.

minimum at (2/3, -4/3)minimum at (0,0)maximum at (2/3, -4/3)maximum at (0,0)

6. The point (0,0) in the domain of f(x, y) = sin(xy) is a point of ___________

ConstantMaximaSaddleMinima

7. Divide 120 into three parts so that the sum of their products taken two at a time is maximum. If x, y, z are two parts, find value of x, y and z.

x=80, y=30, z=50x=40, y=40, z=40x=38, y=50, z=32x=50, y=40, z=30

8. Consider the circular region x² + y² = 81, What is the maximum value of the function?
f(x, y) = x⁶ + y²(3x⁴ + 1) + x².(3y⁴ + 1) + y⁶

901008081 + 813

9. Given f (x,y)=e^x cos⁡y, what is the value of the fifth term in Taylor’s series near (1,\(\frac{π}{4}\)) where it is expanded in increasing order of degree & by following algebraic identity rule?

\(\frac{-e(x-1)(y-\frac{π}{4})}{\sqrt{2}}\) \(\frac{e(x-1)^2}{\sqrt{2}}\) \(-\sqrt{2} e(x-1)(y-\frac{π}{4})\) \(\frac{e(y-\frac{π}{4})^2}{\sqrt{2}}\)

10. Among the following which is the correct expression for Taylor’s theorem in two variables for the function f (x, y) near (a, b) where h=x-a & k=y-b upto second degree?

\(f (a+ h, b+ k) = f (a, b) + \frac{x-a}{1!} f_x(a, b) + \frac{y-b}{1!} f_y(a, b) + \frac{(x-a)^2}{2!} f_{xx}(a, b)\\+2 \frac{(x-a)(y-b)}{2!} f_{xy} (a,b) + \frac{(y-b)^2}{2!} f_{yy}(a, b)\) \(f (a+ h, b+ k) = f (a, b) + \frac{x-a}{1!} f_x(a, b) + \frac{y-b}{1!} f_y(a, b) + \frac{(x-a)^2}{2!} f_{xx}(a, b)\\+ \frac{(x-a)(y-b)}{2!} f_{xy} (a,b) + \frac{(y-b)^2}{2!} f_{yy}(a, b)\) \(f (a+ h, b+ k) = f (a, b) + \frac{x-a}{1!} f_x(a, b) + \frac{y-b}{1!} f_y(a, b) + \frac{(x-a)^2}{2!} f_{xx}(a, b)\\+2 \frac{(x-a)(y-b)}{4!} f_{xy} (a,b) + \frac{(y-b)^2}{2!} f_{yy}(a, b)\) \(f (a+ h, b+ k) = f (a, b) + \frac{x-a}{1!} f_x(a, b) + \frac{y-b}{1!} f_y(a, b) + \frac{(x-a)^2}{2!} f_{xx}(a, b)\\+ \frac{(y-b)^2}{2!} f_{yy}(a, b)\)

11. What is the maximum value of the function f(x, y) = 3xy + 4x²y² in the region?
x=0; y=0; 2x + y = 2

1100100

12. The maximum value of the function is?
f(x, y) = sin(x).cos(2y).cos(x + 2y) + sin(2y).cos(x + 2y).cos(x) in the region x=0; y=0; x+2y = 3

cos(1)sin(1).cos(1)sin(3).cos(3)90

13. Find the minimum value of the function f(x, y) = x² + y² +199 over the real domain.

19901213

14. Discuss minimum value of f(x,y)=x² + y² + 6x + 12.

-939

15. Maximize the function x + y – z = 1 with respect to the constraint xy=36.

80No Maxima exists-8

16. The drawback of Lagrange’s Method of Maxima and minima is?

Nature of stationary point is can not be knownNature of stationary point is known but can not give maxima or minimaAccuracy is not goodMaxima or Minima is not fixed

17. Consider the points closest to the origin on the planes x + y + z = a.

Varies as a2, away from the origin.The closest point travels nearer as a is increasedThe closest point travels farther as a is increasedThe closest point is independent of a as a is not there in the expression of the gradient.

18. What is the maximum value of the function f(x, y) = x²(1 + 3y) + x³ + y³ + y²(1 + 3x) + 2xy over the region x=0; y=0; x + y=1.

-12Has no maximum value0

19. Find the critical points of the function.
f(x, y)=\(\frac{sin^{-1}(y^2).(y^2+3y).(sin(y^6+7y))}{(y^9+y^{10})}+10x\)

(0,0)None exist(0,-90)(90, 0)

20. What is the saddle point?

Point where function has minimum valuePoint where function neither have maximum value nor minimum valuePoint where function has zero valuePoint where function has maximum value

21. If the Hessian matrix of a function is zero then the critical point is?

Depends on FunctionAlways at Origin(100,100)It cannot be concluded

22. The extreme value of the function f(x₁, x₂,….. x_n)=\(\frac{x_1}{2^0}+\frac{x_2}{2^1}+……+\frac{x_n}{2^{n-1}}\) With respect to the constraint Σ^m_i=1 (x_i)² = 1 where m always stays lesser than n and as m,n tends to infinity is?

12\(\frac{2}{3\sqrt{3}}\) 1 ⁄ 2

23. Taylor’s theorem is mainly used in expressing the function as sum with infinite terms.

MaybeFalseTrueDon't Know

24. Find the maximum value of Sin(A)Sin(B)Sin(C) if A, B, C are the angles of triangle.

–3√3⁄83√4⁄83√3⁄8π⁄8

25. Consider the vertical cone. The minimum value of the function in the region f(x,y) = c is?

1-1constant0

Welcome to Fatskills

Join 4M+ learners. Unlock unlimited quizzes, wrong-answer tracking, flashcards + reminders, study guides, and 1-on-1 challenges.

Create a free account Sign in

900+ exams • Millions of questions • No spam

❤ If you liked Fatskills, consider supporting us by checking out The Life Manuals You Never Got.

🌈 Our mission is to help improve your scores in any subject and exam withonline quizzes, practice tests, study guides, & advice for students. Since 2018.

About | Explore | User Guide | Topics | Subjects | Doubt Solver | Career Aptitude Test | Answers | Free Tools | OSHA Basics Quiz | What Should We Know?
Privacy | Terms |

All trademarks, logos and brand names are the property of their respective owners. All company, product and service names used in this website are for identification purposes only. Use of these names, trademarks and brands does not imply endorsement.

25 Questions

❤ If you liked Fatskills, consider supporting us by checking out The Life Manuals You Never Got.

About | Explore | User Guide | Topics | Subjects | Doubt Solver | Career Aptitude Test | Answers | Free Tools | OSHA Basics Quiz | What Should We Know?
Privacy | Terms |

Without work one finishes nothing. - Ralph Waldo Emerson
© 2026 Fatskills.com

All trademarks, logos and brand names are the property of their respective owners. All company, product and service names used in this website are for identification purposes only. Use of these names, trademarks and brands does not imply endorsement.

25 Questions

❤ If you liked Fatskills, consider supporting us by checking out The Life Manuals You Never Got.

About | Explore | User Guide | Topics | Subjects | Doubt Solver | Career Aptitude Test | Answers | Free Tools | OSHA Basics Quiz | What Should We Know? Privacy | Terms |

Without work one finishes nothing. - Ralph Waldo Emerson© 2026 Fatskills.com

All trademarks, logos and brand names are the property of their respective owners. All company, product and service names used in this website are for identification purposes only. Use of these names, trademarks and brands does not imply endorsement.

About | Explore | User Guide | Topics | Subjects | Doubt Solver | Career Aptitude Test | Answers | Free Tools | OSHA Basics Quiz | What Should We Know?
Privacy | Terms |

Without work one finishes nothing. - Ralph Waldo Emerson
© 2026 Fatskills.com