Mathematics · Calculus
Let f: ℝ2 → ℝ be a twice continuously differentiable non-zero function such that f(tx1, tx2) = t3 f(x1, x2) for all t > 0 and (x1, x2) ∈ ℝ2. Which of the following equations is necessarily true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
Share:
- 1x12 ∂2f∂x12(x1,x2) + x22 ∂2f∂x22(x1,x2) + 2x1x2 ∂2f∂x1∂x2(x1,x2) = 9f(x1,x2)
- 2x12 ∂2f∂x12(x1,x2) + x22 ∂2f∂x22(x1,x2) + 2x1x2 ∂2f∂x1∂x2(x1,x2) = 6f(x1,x2)✓
- 3∂f∂x1(1,-1) - ∂f∂x2(1,-1) = 3f(1,-1)
- 43 ∂f∂x1(1,1) + 3 ∂f∂x2(1,1) = f(1,1)
Correct answer
x12 ∂2f∂x12(x1,x2) + x22 ∂2f∂x22(x1,x2) + 2x1x2 ∂2f∂x1∂x2(x1,x2) = 6f(x1,x2)
Download Single Question PDF
Save this question and verified answer as a clean study sheet with live clickable link.
👥
Share with Friends & Study Groups
Challenge your peer aspirants on WhatsApp or Telegram to solve this question!
Online Test Series
Start Free Mock Test →Preparing for Mathematics?
Practice full-length mock tests with real exam timers, instant score analysis, and all-India ranking.
Chapter Practice
Practice Calculus MCQs →Want more practice questions on Calculus?
Solve complete topic-wise tests with detailed solutions on GkGet.
Related Practice Questions
Recommended practice questions in Mathematics · Calculus