For the function, evaluate the following. f(x, y) = 0.7x + 0.5y - 0.05xy %3!

Q: find all possible functions with the givenderivative. y' = x3

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Q: use the graph of y=f(x)y=f(x) to sketch the graph of its derivative f′(x).

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Q: For the following exercises, find the average rate of change of each function on the interval…

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Q: (d) Find the interval(s) where f(x) is decreasing.

A: There are mainly two ways roughly by which a function's behavior can be obtained and first method is…

Q: For the following exercises, find the local and absolute minima and maxima for the functions over…

A: Given function y=3x4+8x3-18x2 find the local and absolute minima and maxima for the function over…

Q: For the following exercises, find the local and/or absolute maxima for the functions over the…

A: First we try to find the local Maxima of f(x) using the second derivative test. Then to find the…

Q: For the following exercises, use the second derivative test to identify any critical points and…

A:

Q: For the following exercises, find the local and/or absolute maxima for the functions over the…

A: Solving by procedure of second derivative test we have

Q: Find the family of antiderivatives for the function, f(x) = 8 12x. Which of these pass through the…

A: To find the family of antiderivatives for f(x) integrate f(x) with respect to x.

Q: of Find - for the following function. and 5xy f(x.y) = e In (3y)

A: Given: Now,        ∂ ∂ xe5xyln3yTreat y as a constant=ln3y∂ ∂ xe5xy=e5xy∂ ∂ x5xy=ln3ye5xy· 5y

Q: For the following exercise, find the average rate of change of each function on the interval…

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Q: Find Fxxygy for the function Fory)-J*J€nx-x]

A: We havr to find the derivative.

Q: For a host - parasite relation, it was determined that when the host density (number of hosts per…

A: y = 1000 x10 + 43 x,where,y = No. of hosts that have parasite,x = No. of hosts per unit area

Q: Find dy for the following functions. y=6x2

A: We have the given function as   y=6x2 We have to differentiate it

Q: For function f (x, y) y? x2+1 Find the maximum rate of decrease of f at the point (1, 2)

A:

Q: For the following functions find Əx²’dy²’ dxðy'ðyðx f(x, y) = x² + y²

A: Answer is given in next step.

Q: find all possible functions with the givenderivative. y' = 5 + 1/x2

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Q: Differentiate the function In e* 8.) y = ex 7.) f(x) = e** – In :

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Q: For the following exercises, use the definition of a derivative to find f′(x). 55.  f(x)=2−3x

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Q: Find the point of diminishing returns (x,y) for the function R(x), where R(x) represents revenue (in…

A: Point of diminishing return is the point where the marginal return starts to diminish. Point of…

Q: Find for the following function. dx2 y=e -6x2 %3D dx2

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Q: For function f(x) = 2" , state a) the average rate of change from x =1 to x=5 b) the instantaneous…

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Q: Calculate L6 for f(x) = v7x + 2 over [1,3]. (Give your answer to three decimal places.)

A: The given function is fx=7x+2 and the interval is 1,3. Obtain the length of the rectangle as…

Q: Differentiate the function.   y=e^0.5t

A: Refer to the question, we have to find the derivative of the provided function y = e^0.5t.

Q: 1. Plot the function f(t): (x+5) for -35 x 5. 4+3x2

A: Plotting graph by finding slope.

Q: For the function y df-1 f(x) = a? – x + 2, x > 0.5, find dy y=10 (f-1)'(10).

A:

Q: For the function f(x)=e5x+e−x defined on the interval(−∞,1], find all intervals where the function…

A: Find all the intervals for where the function is increasing and decreasing

Q: For the following exercises, use the second derivative test to identify any critical points and…

A:

Q: For the following exercises, find the local and absolute minima and maxima for the functions over…

A: the given function is

Q: For the following exercises, find for each function. dx

A: Given, y = x2cosx4  We have to find dydx

Q: For what x-value is the function y = |x+5| not differentiable?

A:

Q: Calculate L6 for f(x) = √√7x + 3 over [1, 3]. (Give your answer to three decimal places.)

A: The given function fx=7x+3 over the interval 1,3 we have to the left Riemann sum using 6…

Q: Calculate L6 for f(x) = v5x + 3 over [1,3]. (Give your answer to three decimal places.) L6 =

A:

Q: 2) For the function below f(x)=7x1.1^x, estimate f'(x) using h=0.001 for the following three values.…

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Q: Give the interval where y is decreasing y=x²e^x

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Q: For the following exercise, find the average rate of change of each function on the interval…

A: We will find the average rate of change of given function as shown below

Q: Find the interval on which f(x) =x'e is increasing.

A: We find f'(x) using the product rule

Q: Find dy for the following functions (メ+リ)+(メーツ)ニxャガ 4.

A:

Q: For the following exercises, use the second derivative test to identify any critical points and…

A:

Q: The average change of the function y = √x from x = 4 to x =16 is _________________ ?

A: The given function y=sqrt(x). We need to find the average change of function over interval [4,16].

Q: For the function, find the average rate of change of f from 1 to x: (f(x)-f(1))/(x-1), x (not equal…

A:

Q: For the following exercises, find the average rate of change of each function on the interval…

A: Explanation of the solution is given below...

Q: For the given function f(x,y)=x²y³+3x³y, find a flay

A:

Q: For the function y = 5x3- 4x a. Determine the average rate of change between x1 = 3 and x2 = 5.  b.…

A: given function y=fx=5x3-4x

Q: For the following exercises, use the second derivative test to identify any critical points and…

A:

Q: y = 1(x − x^2) over (0,1)

A: Let the function be, y=x-x2 Differentiate the function y=x-x2 with respect to x. dydx=1-2x Put 1-2x…

Q: The antiderivative of the function f(x) = .3+9x is

A: find the anti derivative (integral) of fx=56 .3+9x3

Q: For the function y = (f ¹)'(-4)= f(x) = x² + 4x - 3, x ≥ - 2, find df-1 dy y=-4

A: Introduction: For a function y=fx, its inverse function is represented as x=f-1y. It is not…

Q: For the following exercises, use the second derivative test to identify any critical points and…

A: according to our guidelines we can answer only three subparts, or question and rest can be…

Q: For the following exercises, find the local and/or absolute maxima for the functions over the…

A:

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.