Find all the second order partial derivatives of the given function. 10) f(x, y) = (x2 + y2)7
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- find the derivative of (z+j)? j2:+2z z4+ j4z³+6z² – j4z+1 j2:2-2z 24+j4z–6z2 – j4z+1 j2:+2z 24+j4:-6z2+j4z+1 j2:2 -2z z4 - j4z+6z² – j4z+1Select the option that gives a list of the stationary points of the function: f (x,y) = x3 + 3x2 - 3xy2 + 12xy - 9x + 1 A. (2,0) (1,-1) (3,-1) B. (-1,2) (0,1) (0,3) C. (-1,3) (0,2) D. (2,-1) (1,0) (3,0) E. (0,2) (-1,1) (-1,3)5c) Find the partial derivatives? y = 2x2+3xz+85w-8z2
- The function is the revenue function for selling widgets and gizmos with demand price functions PriceGizmos = 27 * 0.91QuantityGizmos/100 QuantityWidgets 290 QuantityGizmos PriceWidgets = 18 * 0.889uantityWidgets/150 230 and, P = (QuanityGizmos, QuantityWidgets) = (784, 395) and P2 = (746, 418)Find the second-order partial derivative. 4) Find fxy when f(x,y) = 8x3y - 7y2 + 2x. A) - 28 C) 24x2 B) - 14 D) 48xy Find , and classify the relative extrema of the function, if they exist; and state the x value where they exist. 5) f(x) = - x2 - 4x + 96Find the derivative of the function. 4. Az) = 6x (9 - 8x)* O (-12x) (9 - 8x)(6x-9) O (-182 )(9 - 8x) (8x – 9) O 48x(9 - 8x)3 3 (- 36x) (9 - 8x) (8x- 3) O (12x) (9 - 8x) (6x- 9) « Previous
- Find the directional derivatives of the convex function f(x) = max{−5x + 3, 2x + 1}.Both first partial derivatives of the function f(x,y) are zero at the given points. Use the second-derivative test to determine the nature of f(x,y) at each of these points. If the second-derivative test is inconclusive, so state. f(x,y) = -9х + 18ху - у + 81y; (- 3, - 3), (9,9) What is the nature of the function at (- 3, - 3)? O A. f(x,y) has neither a relative maximum nor a relative minimum at (-3, - 3). B. f(x,y) has a relative maximum at (- 3, - 3). C. f(x,y) has a relative minimum at (- 3, - 3). D. The second-derivative test is inconclusive at (- 3, – 3). What is the nature of the function at (9,9)? O A. f(x,y) has neither a relative maximum nor a relative minimum at (9,9). B. f(x,y) has a relative minimum at (9,9). O C. f(x,y) has a relative maximum at (9,9). O D. The second-derivative test is inconclusive at (9,9).Find the four second partial derivatives of the following function f(xy)-In (7x2 + y2 +9)
- 1. Is L = {1 − 2x + 3x^2, x − 2x^2, 2 − 5x + 8x^2} linearly independent? If yes, show why. If not, show a dependence relationship. Is L = {1 + 2x + 2x^2, x − 2x^2, −2 − 3x − 5x^2} linearly independent? If yes, show why. If not, show a dependence relationship.Find the critical points of the function by using algebraic techniques (completing the square) or by examining the form of the equation. Verify your results using the partial derivatives test. fx, у) %3D —х? —- 8y2 + 6х — 16у - 8 (х, у, 2) %3D 3, – 1Find f and f, and evaluate each at the given point. y' ху f(x, у) 3 (9, -9) X - y f,(x, y) %3D Fy(x, y) %3D fx(9, -9) = %3D f,(9, -9) %3D