If f(x, y) is a homogeneous function of degree 2 with f'(2, 3) = 4 and f'(4, 6) = 12, find f(6, 9):
Tap an option to check your answer.
UGC-NET 2023 Question 21: Multivariable calculus
Answer and worked solution
Checking your account…
Multivariable calculus has come up 32 times in 7 exams since 2007.
What this question tests
This question is on Homogeneous functions and Euler's theorem, part of Multivariable calculus in Mathematics.
Functions that scale in a fixed way when all inputs scale, and the identity this gives.
TestStop has 12 past-paper questions on this subtopic; the nearest in year are below.
Similar questions from other papers
- Match the partial derivative of function Z = x² + xy² + y. List I A. Zₓ B. Z_y C. Z_(xy) D. Z_(yx). List II I. 2y II. 2yx + 1 III. 2x + y² IV. 2y. Choose the correct…
- Consider the function G(x,y,z)=0. This function allows us to implicitly define each of three variables as a function of the other two variables. Assume that all partial…
- Let f(x,y,z) = x² y³ z. Then, x(∂ f)/(∂ x)(x,y,z) + y(∂ f)/(∂ y)(x,y,z) + z(∂ f)/(∂ z)(x,y,z) =
- If Q = f(K, L) is a homogeneous production function of degree one, which of the following satisfies Euler's theorem?
- For the function F:ℝ²→ℝ specified as F(x,y)=x³-y³+9xy, which of the following options is/are correct
Question from the UGC-NET 2023 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.