Allied & ICAR Exam Bank • ALLIED_2653 MCQ • 1 Mark

Section 1: Engineering Mathematics

Calculus

Subtopic: Maxima and minima of function with several independent variables

Question Statement:

The function $f(x, y) = x y$ on $\mathbb{R}^2$ at the origin $(0, 0)$ has a:

Options:

  • (A) Saddle point
  • (B) Local maximum
  • (C) Local minimum
  • (D) Inflexion line

Answer Key:

A

Step-by-Step Solution & Explanation

At $(0, 0)$: $f_x = y = 0, f_y = x = 0$. $f_{xx} = 0, f_{yy} = 0, f_{xy} = 1$. The discriminant is $r t - s^2 = 0 - 1 = -1 < 0$. Hence it is a saddle point.
← Previous (ALLIED_2652) Next (ALLIED_2654) →

Practice In Authentic CBT Exam Interface

Test your skills under authentic timed conditions with live scoring and AIR percentile ranking.

Launch CBT Mock Test