Find the critical numbers of the function.
y ? 6 |
y2? 2y + 12 |
2. Define a function g: R3 +R by g(x, y, z) = 2x2 + y2 + x2 + 2xz – 2y – 4. (a) Find all the critical points of g. (b) Compute the Hessian H, of g. (c) Classify the critical points of g. (d) The surface g(x, y, z) = 0 is an ellipsoid . Use the method of Lagrange multipliers to find the maximum value of the function (5 marks) (5 marks) (5 marks) f(x, y, z)...
6. Find all extrema of the functional J(y) = 1 + (y2 + 2y) da with boundary conditions y(0) = 0 and y(1) = 0, and subject to the constraint 1(x) = [ (12 + 4y) dx = 1.
Solve the given equation. Find y as an explicit function of x, if possible 2y' y2-1 = x Solve the given equation. Find y as an explicit function of x, if possible y+xe x y' = X
Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) h(p) = (p-3) / (p^2 + 6) Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) g(y) = (y-5) / (y^2 - 3y +15)
6. Find an equation of the tangent plane to the surface z = 4x2-y2 +2y at (-1,2,4) = V20-下一77 at (2,1) 7. Find the linear approximation of f(z. y) and use it to approximte (1.95, 1.08). 8. Find the differential of the function
5. Suppose that a firm's total profit function is P(x,y) = 2xy + 2y+12-(2x2 +y2), where x is amount of production and sales of the first product and y - of the second produc 1) Find all first and second order partial derivatives. 2) Find values of x and y that maximize the profit. Find the maximum profit. 6. Ifx thousand euros is spend on labor and y thousand euros is spend on equipment, the outpu certain factory will be...
PROBLEM 7 Find all critical points of g(x, y) = 12 y - 6xy - 63/2x + 144x + y2 + 3x - 6. Input your answer as a sequence of one or more ordered pairs separated by commas. For example: (1,2), (3,4), (5,6)
6 f(x,y) = -4x2 - y2 +16. – 2y + 1 if any. 6. Find equations of the tangent plane and the normal line to the surface xsin y + z2 - 4= 0 at the point (1,0,2). 7. Find the volume of the solid under the paraboloid 2 = 4 - 2 rer tb.
19. Find the critical points, relative extrema, and saddle points of the function. a. f(x, y) = x2 + y2 +2x – 6y + 6 b. f(x, y) + y2 c. f(x, y) = x2 – 3xy - y2 = x²
(1 point) Find y as a function of t if 2y" + 33y = 0, y(0) = 3, y' (0) = 9. g(t) = Note: This particular webWork problem can't handle complex numbers, so write your answer in terms of sines and cosines, rather than using e to a complex power.