5. Find where the function f (x) xe is increasing, decreasing, concave up and concave down. State the (x, y) coordinates of all relative extrema and inflection points.

Q: Compare the values of delta y and dy for the function f(x)= x^3 - 3 at x=3and delta x= 0.2

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Q: Find and classify all the critical points of the following function: F(x,y)=(3x +4x')( y²+2y)

A: We need to find critical point and classify them.

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

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Q: Examine the function f(x, y) = x³-9xy+y³ +8 for relative extrema and saddle points.

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Q: The critical points of the function f(x, y) = x³ + xy + y² are _____.

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Q: 21) Find the maximum and/or minimum values of f (x, y) = x² + 2xy + 2y² - 6y + 2

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Q: 4. Find f'(x), if f(x) = (2x – 8x²)-²(3x + 1). 5. If y is a twice differentiable function and x cos…

A: Differential equation. Solving only first ques as per bartleby guidelines.

Q: 4.1. Estimate f(3). 4.2. Estimatef'(3). 4.3. Give an equation for the tangent line to y = f(x) at x…

A: To estimate f(3), find the value of y when x=3 from the given graph When x=3, the value of y is 3.5…

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

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

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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: Find the linear approximation L(x) to y = f(x) near x = a for the function.  F(x) = (1 / x) , a = 2

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Q: 11. Find the linear approximation of f(x) = √√x_ at a = 1. Use the linearization to estimate the…

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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: 8. Find the extremum and saddle points of the function f(r, y) =r' - 3ry + y if any.

A: Due to Bartleby guidelines, only 1st question can be answered if multiple questions have been asked.…

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

A:

Q: 4. Suppose that F(t) is a differentiable function of one variable. Define the function z(x, y) = e'F…

A: z(x,y) ey F (exy )diff wrt xdzdx = ey F' ex/ye.1/yzx = ey.ex/yyF' (ex/y)and diff wrt ydzdy= ey…

Q: A) Find and classify the critical points of f(z, y) = x³ + y3 – 6y? – 3.x + 9 using the first and…

A: Note: As per bartleby instruction when more then one question is given only one has to be answered.…

Q: Let f(x, y) = 2x² + 2xy+ y² – 6x + 2y be given. Find and classify critical points of the given…

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Q: Find the linear approximation to f(x) = at a = 4.

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

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Q: Find the critical points of the function f(x,y)=x^(4) + y^(4) − 144xy

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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: (8) Find the linear approximation of the function f(x) = Va at a = 25 and use it to approximate the…

A:

Q: 1. Find any relative extrema of the function by first finding the critical points and then applying…

A: Solution is here

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: Find the linear approximation L(x) to y = f(x) near x = a for the function. f(x) L(x) =

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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: 4. Find the critical points for the function f(x, y) = x² +y³ + 2xy – 2x – 7y. (You do not need to…

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Q: 1 Find the length of the curve f(x) + from x = 2 to x = 4. %3D 6. 2x

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Q: Suppose f and g are two differentiable functions such that f(9(x)) = x? and supposed the equation of…

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Q: For the given function f(x, y) = y2 + xy −(1/6)x3 + 3x, find all of its relative extrema and saddle…

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Q: Examine the function f (x, y) = x3 − 6xy + y3 for relative extrema and saddle points.

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Q: Find out all the relative minimum and maximum values, and sadle points of the function h defined by…

A: Here we have h(x,y)=x3-3x+3xy2 .............................................. (1)

Q: Find the linear approximation L(x)of f(x)=x^4 at the point a = −5 L(x)=

A: Given that f(x) = x4 We have to find the linear approximation L(x) of f(x)=x4 at the point a= -5.

Q: 3. The cost C of manufacturing transformers in a factory varies with the output N per day according…

A:

Q: Examine the function for relative extrema. (If an answer does not exist, enter DNE.) f(x, y) = 9x² +…

A: Discriminant of the functionif we have fxx,fyy,fxythen D=fxxfyy-fxy2if D>0 at (x,y)  anf fxx>0…

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

A:

Q: 5. Find the local extreme values of f(x, y) = x²y on the line a +y = 3.

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Q: 4. Determine the minimum value of the function y = f(x) defined implicitly in the equation x² + 3xy…

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Q: 4. Suppose that y = y(x) is a differentiable function which is defined near x = 2, satisfies y(2) =…

A: Given x2+3xy2+y3=9y2=-1

Q: (3) Find and classify the critical points of the function 6y? f(r, y) = 3y – ry + +2, I#0. %3D

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Q: 1)Classify the critical points of the function f(x,y)=x²+y³+x²y+4

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Q: 3. If f(x) = (1–- t²)e*dt, on what interval is the curve y =f(x) upward? concave

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Q: Find the relative maximum and minimum values. f(x,y) = x° +y° - 3xy

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Q: Find the absolute maximum and minimum values of f(x, y) = x^2 +xy + y^2 - 3x + 3y on the triangular…

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

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Q: Find the extremum and saddle points of the function f(x; y) = x^3 -3xy + y^3 if any.

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