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Solved Maxima and Minima Problems – PDF Download + Concept Summary

 

Questions on Maxima and Minima

Topic: Maxima and Minima – Calculus | Engineering Mathematics

  1. Find the maximum and minimum value of the function f(x, y) = x² + y² − 2x − 4y + 6.
  2. Find the maximum and minimum values of f(x, y) = x² + y² subject to the constraint x + y = 1.
  3. Find the stationary points of f(x, y) = x³ + y³ − 3xy and determine their nature.
  4. Find the local maxima, minima, and saddle points of the function f(x, y) = x² − y².
  5. Find the maximum value of u = xy when 2x + 3y = 6.
  6. Find the absolute maximum and minimum values of f(x, y) = x² + y² on the rectangle 0 ≤ x ≤ 2, 0 ≤ y ≤ 3.
  7. Find the point on the plane x + y + z = 6 closest to the origin.
  8. Find the maximum value of f(x, y) = x²y subject to the constraint x² + y² = 1.
  9. Find the minimum value of f(x, y) = x² + y² − 4x − 6y + 13.
  10. Find the stationary point of f(x, y) = x⁴ + y⁴ − 4xy + 1.

Note: These questions cover unconstrained optimization, constrained optimization (Lagrange’s method), and geometric interpretation of maxima and minima.



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