GATE 2023 ST – Question 29

Calculus · Multivariable Calculus · 1 mark · Numerical answer

Find the maximum of f(x,y)=xy on x²+2y²=1. Round to two decimals.

Show answer and explanation

Correct answer: 0.32 to 0.38

Explanation

The inequality 2√2|xy|≤x²+2y²=1 gives xy≤1/(2√2). Equality is attained with x=1/√2,y=1/2. Therefore the maximum is approximately **0.35**.

GATE 2022 ST Q14 – Define f(x,y)=x²y/(x²+y²) off (0,0),and f(0,0)=0. Which holds on ℝ²?
GATE 2022 ST Q63 – A point P=(x,y,z) lies on z=xy+5 and x+y+z=1 and is nearest to the origin. Find its…
GATE 2021 ST Q55 – Let f(x,y)=8x²−2y. If M,m are its maximum and minimum on x²+y²=1,find M−m,to two decimals.
GATE 2026 ST Q36 – For f(x₁,x₂)=2x₁⁴+x₂²+x₂x₁², which holds?
GATE 2026 ST Q49 – Define f(x,y)=(x³+y³)/√(x²+2y²) away from the origin and zero at the origin. Which hold?
GATE 2025 ST Q37 – On U=(x,y):x+y≤2, find the minimum of f(x,y)=(x−1)⁴+(y−2)⁴.