B. Find and classify the extreme points of function f(x, y) x* +y-4xy-1.

Q: Find and sketch the domain of f(x, y) = √√1 − (x + 1)² − y² + 2 ln (x − y + 1).

A:

Q: Show that the function f(x) = e¯*/2 has inflection points x = f1. at

A: We have the given function as fx=e-x22              ⋯⋯1 As we know that, a point of inflection of…

Q: Let f(x, y) = - 4xy² – 2x² + 8y². Find and classify the critical points of f.

A:

Q: Consider the function F(x, y) = x + 3x2 - 6xy? +2y3, Find critical points (FoC). Identify these…

A: Given function  F(x,y)=x3+3x2-6xy2+2y3 a. Differentiating F partially w.r.t to x and y, we get…

Q: Find the global extrema of f(x)=x2e−x on the interval [−1,1].

A: Given function is

Q: 1. Find and sketch the domain of f(x, y) = (x – 3y)t.

A: For the solution of the problem follow the next step.

Q: Determine the set of points at which the function is continuous. a) f(x,y) = ln (x² + y² – 4)

A: According to question given thatf(x,y)=ln (x2+y2-4)

Q: Q2) Find all local Extreme and Saddle points of the 2x-2y +y +4 function f(x,y)-xy-x-y

A:

Q: If y = f(x) is an odd differentiable function defined on (-o, 0) such that %3D f'(3) = -2 then…

A: A function f(x) is said to be even if f(-x) = f(x) And odd if f(-x) = -f(x)

Q: Find and classify the critical points of the function f(x, y) = 4x²y - 2x - y².

A: We need to determine and classify the critical points of the function: f(x, y)=4x2y-2x-y2.

Q: Find the linearization L(x)  of the function f(x) = x^4 -2x^2+3  at  x =0.

A:

Q: Locate and classify all the critical points of the function. (If an answer does not exist, enter…

A:

Q: 8. Find the extremum and saddle points of the function f(x, y) – x3 – 3xy + y3 if any.

A:

Q: Find the absolute maximum and minimum of the function on the given domain. f(x,y) = 5x + 8y on the…

A:

Q: Find the linearization of the function given below at the specified point. f(x) 4 In(x) at a = 1…

A:

Q: Find the linearization L(x) of the function at f(x) = x4 + 2x2, a = 1 L(x) =

A:

Q: Picture attached. Thanks in advance!

A:

Q: Find all the local maximum, minimum and saddle points for f(x,y) = x³ – 3x + 3xy²

A: Suppose that a,b is critical point of fx,y and its second order partial derivative is continuous…

Q: f(x, y) = 4x² – y²

A:

Q: B1. Verify fy = fx for the function f(x,y) = ln(2x- 3y). %3D xy

A:

Q: Find and classify all critical points for the function f(x, y) = x + y – 4xy + 2 %3D

A:

Q: -Q3/As the function f(x,y) = at (-1,2) xy 1 + x² + y² is Continuous

A: Here we have to check the continuity of the function at the given point.

Q: Locate and classify all the critical points of the function. (If an answer does not exist, enter…

A: We will find the critical points.

Q: Find the linearization of the function given below at the specified point. f(x) 2 In(x) at a = 1…

A:

Q: Find and classify the critical points of the function f(x, y) = x²y+ 4xy – 2y².

A:

Q: f (x, y) = -2x – 4.xy + 2y? + 2x – 2

A:

Q: Find the linearization L(x)of f(x)at x = a where f(x) = Vx² + 9 at a = –4

A:

Q: Find and classify all critical points of each of the function: a.f (x, y) = (x² +x + 1)e¬²/10-y² f…

A: Solution is given below:

Q: (12) Find the local maximum, minimum and saddle points (if any) of the function f(x, y) = x3 – 3x +…

A: Local maximum or minimum of the function

Q: Find and classify the critical points of the function f(x, y) = x³ – y² – 3x + 2y.

A:

Q: 24, Find the domain of H function fw =J 2x+3 -1

A: Given,

Q: 2. Find and classify all the extrema of the function f (x, y) = 4xye e-(x²+y²)/4

A: The given function is:  f(x,y) = 4xy e-(x^2 +y^2)/4

Q: For the function f(x,y) = –x² – xy – y² + 3x + 3y + 4, find and classify all critical points.

A:

Q: Locate the absolute extrema of the function on the closed interval. (a) f(t) = ₂, [3,5] (b) f(x)=…

A: The given functions,a) ft=tt-2, 3,5b) fx=x3-12x, 0,4

Q: Find a point c satisfying the conclusion of the MVT for the function y(x) = 16/x on the interval [0,…

A:

Q: -2 In(x) Consider the function f(x, y) 3y

A:

Q: Find and classify the critical points of the function f(x,y) = x²y+ 4xy – 2y²

A: The given function is f(x,y) =x2y+4xy-2y2.

Q: f(x, y) = 3xy – x²y- xy?

A:

Q: Use the linearization of f(x) 1 at x = 4 to approximate f(4.3) . - f(x) =

A:

Q: The function f(x, y) -{¹. - x² - y², 0, if if x² + y² 1 , is continuous

A: Given function is fx,y=1−x2−y2, if x2+y2≤10,             if x2+y2>1. We have to check whether the…

Q: Find and classify all critical points of the function f(x, y) = x³ + y³ – 3ry – 1.

A: Given: The function is  f(x, y)=x3+y3-3xy-1   To determine: The critical points of the function and…

Q: Describe the domain and range of the function. f(x, y) = In(xy-1) Dor

A:

Q: Find and sketch the domain of the function. f(x, y, z) = ln(64 − 4x2 − 16y2 − z2)

A: Given function is      f(x,y,z) = ln(64-4x2-16y2-z2) We have to find the domain of this function.

Q: Q1// Find and sketch the Domain of f(x,y) In (x' y)

A:

Q: Given f (x,y) = 3 – 2x² – 2xy – 2y² – 16x, find and classify all critical points of f. -

A: Calculate fx, fy , fxx , fyy , fxy for f(x,y)=3-2x2-2xy-2y2-16x as follows.…

Q: Let f(x, y) = -e2"-y + In(3x – y). Find the domain of this function.

A:

Q: "The function f(z) = x2 + i(2y + x) is nowhere analytic" is this statement true or false

A: If the function f(z) = x2 + i(2y+x) is analytic then it must satisfy Cauchy Riemann equation. Here,…

Q: Locate and classify all the critical points of the function.(If an answer does not exist, enter…

A: We need to classify all the critical points of the given function.

Q: (a) f(x) = x² – 2x , [0, 5] (b) f(x) = x³ – }z² , [–1, 2]

A: