Advertisements
Advertisements
Question
If f(x, y) = 3x2 + 4y3 + 6xy - x2y3 + 7, then show that fyy (1,1) = 18.
Solution
Given f(x, y) = 3x2 + 4y3 + 6xy - x2y3 + 7
Differentiating partially with respect to 'y' we get,
`"f"_"y" = (del"f")/(del"y") = 0 + 12y^2 + 6x(1) - x^2(3y^2) + 0`
= 12y2 + 6x - 3x2y2
Differentiating again partially with respect to 'y' we get,
`"f"_"yy" = (del^2"f")/(del"y"^2) = 24y + 0 - 3x^2 (2y) = 24y - 6x^2y`
∴ fyy (1, 1) = 24(1) - 6(1)2(1) = 24 - 6 = 18
Hence proved.
APPEARS IN
RELATED QUESTIONS
Find the marginal productivities of capital (K) and labour (L) if P = 8L – 2K + 3K2 – 2L2 + 7KL when K = 3 and L = 1.
If the production of a firm is given by P = 4LK – L2 + K2, L > 0, K > 0, Prove that L `(del"P")/(del"L") + "K"(del"P")/(del"K")` = 2P.
If the production function is z = 3x2 – 4xy + 3y2 where x is the labour and y is the capital, find the marginal productivities of x and y when x = 1, y = 2.
For the production function P = 3(L)0.4 (K)0.6, find the marginal productivities of labour (L) and capital (K) when L = 10 and K = 6. [use: (0.6)0.6 = 0.736, (1.67)0.4 = 1.2267]
The demand for a quantity A is q = `13 - 2"p"_1 - 3"p"_2^2`. Find the partial elasticities `"E"_"q"/("E"_("p"_1))` and `"E"_"q"/("E"_("p"_2))` when p1 = p2 = 2.
The demand for a quantity A is q = `80 - "p"_1^2 + 5"p"_2 - "p"_1"p"_2`. Find the partial elasticities `"E"_"q"/("E"_("p"_1))` and `"E"_"q"/("E"_("p"_2))` when p1 = 2, p2 = 1.
Verify `(del^2 "u")/(del x del "y") = (del^2 "u")/(del "y" del x)` for u = x3 + 3x2 y2 + y3.
If R = 5000 units/year, C1 = 20 paise, C3 = ₹ 20 then EOQ is:
