Suppose you had an inverted “U-shaped” function. Describe what the first and second derivatives would tell you
Suppose you had an inverted “U-shaped” function. Describe what the first and second derivatives would tell...
Find all the first and second-partial derivatives for the utility function, U -50x 5y 0.2 (a) Give a verbal description of each derivative. (b) Are the marginal functions increasing or decreasing. Use the derivatives to justify your answer b. Given the function Q- Al'KB, explain the terms: constant returns to scale; increasing returns to scale; decreasing returns to scale. Show that the production function, Q -100L0.3K0.5, exhibits decreasing returns to scale and diminishing returns to labour Show that the production...
for the following function: 3. Find all first and second partial derivatives, of of of of of Ꭷr ' Ꭷy ' Ꭷra ' ayya ' ᎧyᎧr f(, y =re*v
Write the first and second derivatives of the function. f(x) = 4.2 In x + 5.1 f'(x) = . f"(x) =
Find the first and second derivatives of the function. g(x) = -2x3 + 10x2 + 7x - 70 g'(x) = g"(x) = Type here to search o
Find the first and second derivatives of the function. g(x) = -2x3 + 10x2 + 7x - 70 g'(x) = -61? + 20u+7 9"(x) = –12x + 20 Type here to search o
Suppose (1,1) is a critical point of a function f with continuous second derivatives. In each case, what can you say about f? (6 Pts) (a) fxx(1,1) = −3, fxy(1,1) = 1, fyy(1,1) = 2 (b) fxx(1,1) = −4, fxy(1,1) = 2, fyy(1,1) = −1 (c) fxx(1,1) = −4, fxy(1,1) = −2, fyy(1,1) = −2 (d) fxx(1,1) = 4, fxy(1,1) = 3, fyy(1,1) = 3
5. (a) Suppose f is any function with continuous second-order partial derivatives such that f(0,0) = 0 and (0,0) is a critical point of f. Write an expression for the second-degree Taylor polynomial, Q, of f at (0,0).
Suppose that f is a twice differentiable function and that its second partial derivatives are continuous. Let h(t) = f(x(t), y(t)) where x = 2e and y = 2t. Suppose that f:(2,0) = 4, fy(2,0) = 3, fx=(2,0) = 2, fyy(2,0) = 3, and fxy(2,0) = 2. Find out that when t=0.
Compute all the first and second partial derivatives of the function g(r, t) = po cos(3t) - e5r ag ag drðt 02g at2
Find the first partial derivatives of the following function U z) = sin(x47 +92) NUN Enter your answer in each of the answer boxes Type here in