E- Find the extrema of the function f:RR, f(x)= +*; +X;X Determine x + x the nature of the extrema by checking the second order conditions.

Q: f is a differentiable function. Then (х) dx ef(x) + C el(x}+C f'(x)ex) + C f'(x) + e(x) + C f(x)ex)…

A: topic - integration

Q: What does it mean for a function of two variables, f (x, y),to be differentiable at a point (a, b)?

A: A function differentiable at a point has a derivative that is defined at that point. This is defined…

Q: An estimate value of f(x) dx is 10 using trapezoidal 2 - interval rule. W is an estimate value of…

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Q: Locate the absolute extrema of the function on the closed interval. g(x) = x² - 2x, [0, 9] minimum…

A: Given that      g(x) = x2 - 2x ,    [0,9]

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

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Q: b) I =f- x(1+(In x))

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Q: x Find all absolute extrema of f(x, y) = x² + y² – 25 subject to y = y? |

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Q: e function f(x, y) = (x – 1)² + (y – 1)² subject to the constriant

A: The given function is f(x,y)=x-12+y-12 and subjects to the constraint x2+y2=8 the formula for the…

Q: F F) s an antiderivative of x-+x-, then what is the value of F(1)-F(-1)2 -1

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Q: Autocorrelation function is maximum at the origin, i.e., |Rxx (7) |S Rxx (0) XX

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Q: of of For the function f(x,y)% 9x2- 3y°-4, find and dx dy of II

A: While calculating the partial differentiation of a function with respect to X we consider the other…

Q: f(x, y) = x² – y²

A: f(x,y) = x2 - y2 Let us firstly find the first order partial derivatives of the given function.…

Q: The area of the region in the xy-plane enclosed by the x-axis, the curve y = f(x), f(x) 2 0, and the…

A: given: a function y=f(x), f(x)≥0. the area of the region in the xy plane enclosed by the curve…

Q: Find the linear approximation of the function f(x) = V1 – x at a use it to estimate 0.95.I must see…

A: We find f'(x) using power rule and chain rule

Q: - Integrate the function f orgy) =y-Vx over triangle cut from the first quadrant by Line X+y=1

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Q: Vx -Vx x +0 R: Let f(x)=< Vx -1/r +e x=0 Show that f(x) is not differentiable at x = 0.

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Q: e critical point of the function f(, y) - 6 +7x + æ² + 4y – 2y?

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Q: x²-y² x²+y2 (x, y) = (0,0) For which value of "a" the function f (x,y) is continuous? (x, y) = (0,0)

A: Continuity.

Q: Find the absolute extrema of the function f(x, y) = x² + y? – 2x on the triangular region with…

A: The shaded part represents the region with the given vertices. We observe that our critical point…

Q: Find all local extrema for 4 f(x, y): * - 4xy + y.

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Q: Find the most general antiderivative of the function. (Check your answer by differentiation. Use C…

A: Given query is to find the antiderivative if the expression.

Q: .Find extrema for a function y=f(x)%3D2X² - 8x on an interval [0, 6].

A: An extremum (or extreme value) of a function is a point at which a maximum or minimum value of the…

Q: consider the function f(x, y) = esin(= Find the maximum rate of decrease of f at the point

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Q: Find the linear approximation of f(x) = (1 +x)" at x = 0. Use this approximation to estimate (1.01)³…

A: Linear approximation of a function f(x) at x=a is  L(x) =f(a)+f'(a)(x-a), where f'(a) is the first…

Q: The minimum rate of change of the function f(x, y) = In(x² + y²) at the point (-1,0) is: a. -1 O b.…

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Q: ind the local extrema of the function f(x,y)=e* (x² – 2y²) x-y

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Q: 3 Let f(x) = 8x° 1 df 15x - 5, x2 1.5. Find the value of dx at the point x= 2004 = f(7). %3D

A: Known fact: derivative of f-1x=1f' f-1x.

Q: Find all extrema for the function f(x, y) = (x² + y²)e¬x and determine if they are each maximums,…

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

Q: Using linear approximation of f(x,y)=*+Y at (3,2), the value of f(2.94,1.94) estimated to be x-y

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Q: Examine the Function For relative extrema and raddle points. 80 x + 80y-x 2. h(x.y) %3D

A: Consider the function as shown below We have to find the partial differentials of first order of…

Q: Find local extrema  f(x,y)=-x^2-y^2-5x-7

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Q: 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: The general solution of Besseal function is given by y = c,J,(x) +y,(x)

A: Given statement, The general solution of Bessel function is given by y=C1Inx+ynx

Q: Find all local extrema of the function f: R? → R, f(x, y) = x³ + y³ + 3xy.

A: The stationary points are calculated by solving the equations, fx=0 , fy=0 together. The…

Q: Find the absolute extrema of the function f(x, y) = x2 + y? 2x on the triangular region with…

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Q: f(x) is a twice differentiable function with f(0) = 4, ƒ(1) = 3, f'(1) = 6, Then So 3xf" (x)dx =

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Q: Find the absolute extrema of the function f(x, y) = x² + y? – 2x on the triangular region with…

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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 the absolute extrema of the function f(x,y) = xy - x - 3y on the triangular region with…

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Q: · y = Vx - x, (1, 0)

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Q: Find the linear approximation L(x) to y = f(x) near x = a for the function. f(x) = 1 a = 3 L(x) :…

A: The solution are next step

Q: Differentiate the function. y = In(e-X + xe¬X) y' = II

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Q: Compute f -f(g(x)), where f(x) = x° and g(x) = 8x – 1. dx -f(g(x)) =| dx

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Q: What are all the relative extrema and saddle points of the function  f (x, y) = ln(x −y) + x2 + y

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Q: Find a linear approximation to f(x,y) at (-1, 1). [2хy] y Use your result to find an approximation…

A: Given function is fx,y=xy2xy                  (i) To find a linear approximation to the function…

Q: consider a continuous function y = f(x) whose first derivative is y = x(x – 2). It has a…

A: Second derivative Test : when a function slope is zero at 'x' and the second derivative at x is :…

Q: Find the average rate of change of the function f(x)=x2  on the interval [x, x+h]

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Q: 2. Find the number of extrema of the function f(x, y) = (x – 1)² + y² – 4y. If there Is no extrema,…

A: We are asked to find the number of extrema of the function.

Q: The average revenue is defined as the function R(x) R(z) = (x > 0) Prove that if a revenue function…

A: Given average revenue defined as function R¯x=Rxx   x&gt;0 To prove if a revenue function Rx is…

Q: Describe the domain of : f (x,y) = Ln(2 + x + y)

A: in the question it is asked to write the domain of f(x, y)=ln(2+x+y).