Test the function f (x, y) =x² + y' - 3xy +15 for local maxima and minima and saddle points. Find function's value at these points.

Q: Find all critical points of f(x,y) = 1/x - 1/y + xy and classify each as a relative minimum,…

A: We use second order partial derivative test to find relative maximum and minimum, saddle point

Q: Determine the critical points of f(x, y) = 4.xy-a -y". Then, using the Second Derivative Test,…

A:

Q: Find the orthogonal trajectories to the family of curves: x² = C-v'(ln y² –1).

A:

Q: Consider the function f(x, y) = 2x²y²-y4 - 8x² Compute the stationary points of the function f(x, y)…

A: Let us consider the given function f(x,y) To find the maxima and  minima Find the partial…

Q: Determine the second-order partial derivative for the indicated function f(c,y) = cos(2x² – 3y?)…

A: Partial derivative of a function g(x,y) with respect to x is the derivative of g(x,y) keeping y…

Q: Find the indicated partial derivative. f(x, y, z)=euz²; fzyz fxyz(x, y, z) =

A:

Q: second derivative

A: To find the critical point(s) of the function f(x, y) = xy + ln x + 2y^2  Then by  use the second…

Q: i) Find the orthogonal trajectories of the family of curves: y : 1+ x?

A: By Bartleby policy I have to solve only first one as these 2 are unrelated problems

Q: Find all of the critical points of the function f(x, y) = x²y². Can the second derivatives test be…

A:

Q: a?f (or and y. that is, f(x,y) = e² with respect to ayax axay Calculate the second-order partial…

A:

Q: Find the value of ∂z/∂x at the point (1, 1, 1) if the equation xy + z3x - 2yz = 0 defines z as a…

A: Given, the equation xy + z3x – 2yz = 0, defines z as a function of two independent variables x and y…

Q: y = x – 2 + Ce* X-

A:

Q: Find the critical points of the function f(x,y) = y² + x²y+ x² – 2y and use Second Derivative Test…

A: Finding fx, fxx, fy,fyy and fxy and use D(x,y) = fxx . fyy - fxy^2 , to find relative maxima or…

Q: For z = arctan(x² + y²): Compute all first and second order partial derivatives. Find the…

A:

Q: For the function f(x, y) = Vx³ + y³ find both partial derivatives at the point (0,0) (separate by…

A: Given function, f(x,y)=x3+y33

Q: Find the critical point of the function f(x,y)=6x−2y^2−ln(|x+y|). c= Use the Second Derivative Test…

A:

Q: f (x, y) = 3xy(x + 2y – 6) -

A: By second derivative test ,

Q: Find the value of ∂x/∂z at the point (1, -1, -3) if the equation xz + y ln x - x2 + 4 = 0 defines x…

A: Given equation is xz+ylnx-x2+4=0. Given point is 1,-1,-3. Partial derivative of given equation with…

Q: Find the critical point of the function f(x, y) = 2e* – 4xe". c = Use the Second Derivative Test to…

A: To find- critical point and do the second derivative test.

Q: The partial derivative fx(-1,0) of ƒ(x, y) = xe³ + x² + 1 is equal to −1. Select one: True False

A:

Q: Using the method of characteristics, find a solution to the partial derivative equation xux + uy = u…

A:

Q: Compute the partial derivative fxxyz for f(x, y, z) = cos(cos(x3 + z2 )) + x2 ln(y2 + z2 ).

A:

Q: of ) Find the first order partial derivative of and for the function f (x, y) = x/y -x²y+y² ây

A:

Q: What is the mixed, second order partial derivative of this function. f (x, y) = / 2x² + y²

A:

Q: The function f (x, y) = x³y + y3 – 3x?y + 2 has critical points at (0,0), (2,), (2, -) and (3,0).…

A: S

Q: Q#2 Find the relative extrema using both First and Second Partial Derivative test i) f(x) = x* –…

A: Given: A function fx=x4-12x3 To find relative extrema first find critical points and then substitute…

Q: Find the critical points of the functions S(x, y) = x + 2y – 4y + 8x, g(x,y) = x² – 14xy + y Use the…

A:

Q: given the function f(x) = (x+4)^2 + (y-2)^2 (i)find the critical points (ii)using the second…

A:

Q: Determine and classify all relative extrema and saddle points of f (x, y) = 3xy(x + 2y – 6) using…

A:

Q: Find the orthogonal trajectories for the family of curves. (Enter your solution in the form F(x, y)…

A:

Q: Identify the critical points of the function f(x, y) = x³ – 12x +y² – 3xy + 30 and the local minimum…

A:

Q: find the first partial derivative  f(x,y) = squareroot (2x+y^2)

A:

Q: ompute the partial derivative: (1, y) = cos(x+ – 6y) -(0, т) —

A:

Q: Find the critical points of f(x, y) = x³ – 6xy + y³. Use the second derivative test to classify each…

A: For the solution follow the next steps.

Q: Use the second partial derivative test to find the relative extrema of f(x,y) = -x³ + 4xy 2y2 + 1.

A: The given function is  f(x, y)=-x3+4xy-2y2+1

Q: Find the critical point of the function f(x,y)=3e^x−2xe^y. c= Use the Second Derivative Test to…

A: f(x,y)=3ex-2xey First we find critical point from equations fx=0 and fy=0 Then,  Second Derivative…

Q: Find the second-order partial derivative fxx ( x , y ) of the function f ( x , y ) = x 4 y 4 - sqrt…

A:

Q: Find the critical points of the function f(x, y) = y² + x?y+x² – 2y and use Second Derivative Test…

A: Follow the steps below to yield the result . Calculate . Find the critical point by solving the…

Q: f(x, y) = 3xy – x²y- xy?

A:

Q: ) Use the second derivative test to classify each critical point of f (x,y)=-x' +4xy- 2y² +1 as a…

A:

Q: Find all points (x,y) where f(x,y) has a possible relative maximum or minimum. f(x.y) 3x3 +4x2y-36y…

A:

Q: Find the local extreme values ​​(Maximum, Minimum and Saddle Points) of the function f (x, y) = ex *…

A:

Q: Find the critical point of the function f(x, y) = 24x – 4y² – In(|x + y|). - - c = Use the Second…

A: see below the answer and explanation

Q: Consider the function f(x, y) = xy² exp ( - 1/² + y ) 3 Compute the stationary points of the…

A: Given fx,y= xy2exp-x33+y

Q: Q2: Find Partial derivative of the function with the respect with each variable f(x, y) = (x² - 1)(y…

A:

Q: Find the first partial derivative wx, wy, and wz of (x + yw )2 –  ez  – 2 = 0  Make the solution…

A:

Q: Find the partial derivative of fy for the function * 3 f (x, y) = (3x² + y²) ³ 3x² (3x² + y²)²…

A:

Q: Find the critical point of the function f(x, y) = – (25x + 5y² + In(]x + y[). c = Use the Second…

A: As two questions are given, I will solve only one. Given , f(x,y)=-25x+5y2+lnx+y…

Q: Find the critical points for the function: f(x,y)=x3+y3-9x2-48y-3 and use the Second Derivative Test…

A: To determine the critical points for the function and classify the critical points.

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.