The average revenue is defined as the function R(x) Ř(z) (x > 0) Prove that if a revenue function R(x) is concave downward (R"(x) < 0), then the level of sales that will result in the largest average revenue occurs when Ř(x)= R'(x).

Q: 9) Suppose that the total cost of manufacturing x units of a certain commodity is C (x) = 2x? + 6x +…

A: Given function is as below : C(x)=2x2+6x+12 Marginal cost can be given by Derivative of C(x) .…

Q: 1. Find the first partial derivative of z with respect to x if x'y+ y°z+ z'x = 11.

A:

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A: Query- How can we minimise the error of an approximation in a linear approximation at the point…

Q: Find partial derivative føyz of the function f(x, Y, z) = z ln x + 2y

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Q: Find the partial derivative of f with respect to x of the function f(x,y) =xy(e^x3)+y

A:

Q: 26) Find the partial derivative of of f= y cos x+ 2x sin z + 5y with respect to y.

A:

Q: If U = lx+my,v=mx-ly then prove that partial derivative of x

A: Given: u=lx+my v=mx-ly   To show: ux=-vy and uy=vx

Q: find the total derivative of z = f(x,y) = 2x+xy-y2 where x=g(y)=3y2

A: Given function: z=2x+xy-y2 where x=3y2 Putting the value of x in z , we get…

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

A:

Q: 2. Let f(x, y,2) = z-sin(xy), x = t, y = In t, z = e. Find derivative of f directly and by using…

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Q: Calculate differential: f (x) = = e-* cos(3x) + 2 of the range [1,2] with h=0.05 a) Using the…

A: Equation is f(x)=e-xcos(3x)+2.Numerical differentiation method to find the solution.The value of the…

Q: Given f(x, y) = (3x – x2)(2y – y?). (a) Find all the critical points of the function. (b) Classify…

A:

Q: Find the linearization of the function F(x)=tan-1(2x)= arctan(2x) at x=0. Then use linearization to…

A: We know the linearization of the function f(x) at x=a    L(x) = f(a) + f'(x)*(x-a)   In the…

Q: 3. If f(r, y) = x*y - 2x-4y, then the total derivative of f

A:

Q: The functions f (x, y) = x^2 + y^2 and g(x, y) = x^2 − y^2 both have a critical point at (0, 0). How…

A: We have given functions fx,y=x2+y2   and gx,y=x2-y2 We have given 0,0 is a critical point of these…

Q: Solve for the partial derivative with respect to x, y and z f(x, y, z) = x²y + xy² + 2xyz

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Q: Find partial derivative of dx for the function f(x.y) given below exp 2x. siny .(at the point (In2,…

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Q: Suppose that the total cost of manufacturing x units of a certain commodity is C (x) = 2?2 + 6? +…

A: Given, Total cost of manufacturing x units of a certain commodity =  C(x) =  2x2 + 6x + 12 We need…

Q: Let f(x, y,z) = z-sin(xy), x t, y Int, z et1. Find derivative of f directly and by using chain rule…

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

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Q: Find the partial derivative fx ( x , y ). f ( x , y ) = x ln ( 3x + 4y )

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Q: Find the critical point of the function f(x, y) =-(8x+2y2 +ln(|x+y|)). c = Use the Second…

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Q: Find the partial derivative Əz Əx for the function z = 8y²√x.

A:

Q: Find the partial derivative of f(x,y) with respect to y at the point (3,2) f(x,y) = ln(x^2y-xy^2)

A: A partial derivative of a function of several variables is its derivative with respect to one of…

Q: What is the difference between the linearization, L(x), of f at a, and the linear approximation (or…

A: Given question:- What is the difference between the linearization, L(x), of f at a, and the linear…

Q: derivative

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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: From the partial differential eqiuation by eliminating the arbitrary function z=(x2+y2+z2)

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Q: 2. Given that y= -- Use a limit to find the instantaneous rate of change of y with respect to x at…

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Q: * find the dicredional derivative af the. f omc tion and in the direction of a= [o,3, 37 + find the…

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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: If f(x, y) = y² cos(x) – x³ In(y), find the second partial derivative ду дх

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Q: 3. Use the forward-difference formula to approximate the derivative of f (x)=sin(In x) at x, = 2.5…

A: The derivative of the function can be calculated using the difference method. The formula for the…

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Q: A total cost function (in dollars) is given by C(x) = 116 + 3x + 0.37x. Use differentials to…

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Q: Find the partial derivative with respect to x of e^y-2*ln(x)-x^3y^2.

A:

Q: Find partial derivative of: z=f(x,y)= e^x^2+y^2  +   cos(x+y^2

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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

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Q: Find y(1) for y" = - 4z - 4y, X, = 0, yo = 0, z, = 1, with step length 0.1 using Euler method (2nd…

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Q: 2 e -8; x(0) = 1 dt

A: Solution is given below:

Q: The general anti-derivative of the function f (x) - In(x) is given by x In( x)+ C Inx)-x+ C x In(x)…

A: The integral (anti derivative) of fx=lnx can be evaluated by using integration by parts. The…

Q: The functions f(x, y) = x 2 + y 2 and g(x, y) = x 2 - y 2 both have acritical point at (0, 0). How…

A: We have f(x, y)=x2 + y2 and g(x, y)=x2 - y2 By finding the partial derivatives fx=2x, fy=2y, gx=2x,…

Q: Find the Partial derivative of f with respect to y for * f (x, y) = x+y

A: →While calculating ∂f(x,y)∂y , consider 'x' as constant.→∂∂yuv = v∂u∂y-u∂v∂yv2

Q: find the partial derivative of the function with respectto each variable. h(x, y, z) = sin (2πx + y…

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Q: Solve for the partial derivative with respect to x, y and z f(x,y,z) = x²y + xy² + 2xyz

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.