Maths-
General
Easy

Question

# If  is a homogeneous function of order .I) II) III) Which of the above statements is correct ?

Hint:

## The correct answer is: Only I and III

### We are given that u is a homogeneous function of degree  n and it is function of x and y. We will check all three statements one by one.I. For first statement, we will take the partial derivative of u w.r.t x and y. We are using Euler's theorem to write the derivative.Euler's theorem states that if u is homogeneous function of x and y having degree n, then we can write         ...(1)The first statement is correct.II. For second statement, we need second order derivative. We will take the partial derivative of equation (1) w.r.t x and then y.Take partial derivative w.r.t xMultiply the equation (2) by x     ...(3)Similarly, take the partial derivative of equation (1) w.r.t y.Multiply equation (4) by y         ...(5)Adding (4) and (5) we get,From (1) we getSo, statement "II" is incorrect.III. See equation no (2).We can say that statement III is correct.So, the option which says "only I and III", is the right option.

We have to remember all the three results instead of deriving them.