7. Find and classify all stationary points of the function f(r, y) = 1 +y? - 12r + 6y-3

Q: If W[y,, Y2 Y3]=0, then {y1, y2 , y3} must linearly dependent, where y1, y2 , y3 are diffferentiable…

A: To find- If Wy1, y2, y3 = 0, then y1, y2, y3 must linearly dependent, where y1, y2, y3 are…

Q: 1. Find the orthogonal trajectories of the family of curves x? + y2 = cy.

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Q: 2. Find the derivative of the function at PO in the direction of u. f(x,y)=6x-7y, P0(-7,-2), u=4i-3j

A: We have to find derivative

Q: 2. Show that the function u = p(xy) + Vry (y/x) provides the equation y². 0. dy?

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Q: Find the value of " dt 2 at the point (0, -1) if xy + y? = 1 5.

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Q: Let f(x,y) be a differentiable function satisfying the equation = xy. %3D ду af and After the change…

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Q: 3. Find the derivative of the function f(x, y, z) = xy³ + yz³ + zx³ at the point (-1, 2, 1) in the…

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Q: (1) Where on the line r = ay does the function f(x, y) = (x – a)² + (y – 2)2 attain its smallest…

A: The line whose equation is of the form y=mx is passes through the origin and slope of the line is m.

Q: Find all stationary points of the function z = f(x, y) = 3x² – 6xy + 2y³.

A: To find stationary points of the function z=fx,y=3x2-6xy+2y3

Q: Find the orthogonal trajectories of the curve x^(2) + y^(2) = c^(2)

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Q: Find the linear approximation to the equation f(x, y) = 2, at the point (4,2,4), and use it to 2 %3D…

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Q: 11. Find the linear approximation to given function at indicated point (Баллов: 2) x2 z = 3 + +, Po…

A: Topic:- linear approximation

Q: If Wly, , y2. Yal = 0, then (y1, y2 , y3) must linearly dependent, where y1, y2 , y3 are…

A: Given that if  W[y1,y2,y3]=0, then {y1, y2,y3} must linearly dependent, where y1,y2,y3 are…

Q: Q4/ Linearize the Function Z = XY2 About X, = 3, Y, = 6 using: a) Absolute Variables b) Perturbation…

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Q: Q.2 Discuss the function f (x, y) =x'+y'-2(x +y')+3xy for all relative maximum, minimum and saddle…

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Q: 1 A point is moving along the graph of the functiony = dy 9x2 + 6 such that dt = 3 centimeters per…

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Q: 2. Show that the function u = (xy) + JTY v(y/x) provides the equation y² : 0. dy?

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Q: 2. (a) Find the linear approximation L(x, y) near the point (1, 2) of the function f (X,Y)=(0=Y) +…

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Q: Find the ditterential of the function y = (x + 1(5x - 3). Sx-x-5 dy = (Sx - 3) *?+ 6x-5 (5x- 3)? dy…

A: Use the quotient rule of differentiation ddxuv=vdudx-udvdxv2. Power rule of differentiation…

Q: 4. Use the linearization of f(x, y) Vx + 2y to approximate f(3.01,2

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Q: express in the form y = f (x) by eliminating the parameter  x = t 2, y = t 3 + 1

A: Given, parametric equation is:  x=t2,y=t3+1 Solution: x=t2,⇒t=±x     ...(1)y=t3+1 ⇒y=(±x)3+1…

Q: If Wly, Y2 Y3]= 0, then (y1, y2, y3) must linearly dependent, where y1, y2 , y3 are diffferentiable…

A:

Q: 6 Determine the position and nature of the stationary points of the functions: (a) z= 2x²y² + 4xy² –…

A: stationary points are those points of function f(X) where its gradient is ∇f(X) = 0 if hessian…

Q: Find the linear approximation of the function y = x at point xo = 1 .3 О а. у%3D Зх - 2 О Б. у3D 3х…

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Q: 7. The function f(x, y) = 3x² - 6xy² - 4y³ has two stationary points. Find both of them. You are NOT…

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Q: Find the linearization of f(x, y) = −x² + 2y² at the point (3,-1). Use the linearization to estimate…

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Q: The student should determine the minimum rate of change of the function g(x, y) = y²e*Y on the…

A: First I have written the rule of minimum rate of change of a function at given point and then find…

Q: Find the directional derivative fü(9, 2) for the function 37 - 47 5 f(x, y) = xy + y³ with u = fű(9,…

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Q: Supposed that z is defined implicitly as a function of x and y by the equation x2 + y2 +z2 = 4. Find…

A: The given data is: x2+y2+z2=4 To find the value of dzdx

Q: Consider a function of 3 variables h (x, y, z2) = -3 (2+ Calculate the value of its third order…

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Q: What is the equation of the curve y = ax* + bx + cx² + dx + e tangent to y = 25x (2,14), to y = 2x +…

A: By verifying options and substitution of point (-1,11) it is verifying option C

Q: Determine the critical point and its type of function f with f (x, y) = 3x^2y + y^3 − 3x^2 − 3y^2 +…

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Q: The slope of the secant line of the function y =Vx +x through the points x, = 1 and the point xz = 4…

A: y=x+x

Q: Find an equation for the level surface of the function f (x, y) = ln (x² + y²+ z²) that passes…

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Q: Find the linear approximation of the function y = x' at point xo 1 О а. у %3D Зх — 2 -

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Q: Зх +2y The function f(x,y)= is discontinuous at point x +y+1 (5,-3).

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Q: Find the orthogonal trajectories of the family of curves x3y-xy3=c where c is constant

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Q: Show that the function f(x, y) = 3x - 4y² is differentiable at point (−1, 2)

A: answer is in next step. please give a like !!!

Q: Find and determine type of stationary point for f(x,y)= 2x² – 4.xy + y² +x+3y

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Q: Find the directional derivative fü(9, 2) for the function 37 - 47 5 f(x, y) = xy + y³ with u = fū(9,…

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Q: 9. An equation of the line normal to the graph of f(x)=, at (1,–1) is (a) 2x - y -3 -0 (b) 2x + y…

A: Explanation: Given that  f(x)=xx-2 at (1,-1)   Concept Used: To find the normal firstly find the…

Q: Find the linearization of the function z =/ at the point (-5, 1). L(1, y)

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Q: Consider the function f: R²R given by f(x, y) = ³ + ² + 2xy + y2-y. Find and classify all stationary…

A: Here is the solution:

Q: 4. What is the direction in which the function f(x, y) = yx² -- decreases most rapidly at the point…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the direction at which the function f (x, у, 2) %3 хIn(е' — хг) increases fastest at (-3,0,0)

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Q: Find the orthogonal trajectories of the given family of curves x^2 + y^2 = c^2. *

A: Curves:  x²+y²=c²

Q: Find the linearization of f(x,y) at the indicated point (X0.Yo)- f(x,y) = /x + 2y; (1,6) L(x,y) =

A:

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.