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NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Application of Derivatives

NDA 2023 · Mathematics · Application of Derivatives

Given that 4 x^2+y^2=9 What is the maximum value of xy?

Given that 4x2+y2=94 x^2+y^2=9 What is the maximum value of xy?

Options

  1. A94\frac{9}{4}
  2. B32\frac{3}{2}
  3. C49\frac{4}{9}
  4. D23\frac{2}{3}

Correct answer

A. 94\frac{9}{4}

Step-by-step solution

Since, y=±9−4x2y= \pm \sqrt{9-4 x^2} let f(x)=xy=x9−4x2f(x)=x y=x \sqrt{9-4 x^2} So, maximum value of f(x)f(x) is 94\frac{9}{4}
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