For the following exercises, find the x- or t-intercepts of the polynomial functions. 9. C(t) = 2t(t − 3)(t + 1)^2 19. f(x) = 2x^4 + 6x^2 − 8

Q: Here is a quadratic function I made for review: f(x)= x^2 + 4x - 6 What are the x and y…

A: Given Function :

Q: Given U = VXY; and Px=10 , Py-20, income=100; what is the value of MRSxy at the optimization point?…

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Q: Find f(4) using forward, backward and central difference of : (3 – 2x)2 f(x) = x2 Step size = 02 %3D

A: We have to find difference .

Q: What is derivation of f(x) = (2x² – x + 1)³ at %3D Xo = 1 ?

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Q: Find f' (a) for 13x f(x) = 9x + 8 f' (a) =

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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: The total profit P(x) (in thousands of dollars) from a sale of x thousand units of a new product is…

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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…

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Q: The total profit P(x) (in thousands of dollars) from a sale of x thousand units of a new product is…

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Q: For the following exercises, consider a pizzeria that sell pizzas for a revenue of R(x) = ax and…

A: Given R(x) = 10x  and C(x) = 2x + x2

Q: For x 2 0, show that 1S v1+x³ <1+x°. Explain your answers in detail.

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Q: Find the antiderivative of f(x) = x³ – 6x +7

A: fx=x3-6x+7 to find the antiderivative, we need to take an integration Fx=∫ fxdx

Q: The antiderivative of the function f(x) .2+9x is. 8.

A: We use basic integration method to solve this Question

Q: Find the local extrema for f(x) = „5/3 + 8x2/3

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Q: For the following exercise, use the vertex (h, k) and a point on the graph (x, y) to find the…

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Q: is y=s/(1+s)  a rational function? If not, what type of function is it?

A: Given function,  y = s/(1 + s)  To find whether it is a rational function or not.

Q: for f(x)=2x4-5x3+7 find all potential points of inflection and map the intervals where the function…

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

A: Given :f(x,y)=-x2-5y2+10x-30y-62

Q: The antiderivative of the function f(x) =.8+ 11a is -5 2.8x4 +c -5 + 2.8 + c -5 + 2.8x +c -5 .8+…

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Q: The antiderivative of the function f(x) = x2 + 9x is. -5 + 18.0x? + c -5 4.5x? + c -9 + 2.5x² + c -5…

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Q: For the function f(x) = 7x', find f-1(x). %3D or () = E Of (2) = V %3D Subre Of (2) = 7V#

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Q: 2. For the given polynomial function f(x) = -(x² – 4)(x + 1) 9) Find x and y intercepts (Show…

A: A polynomial is given as f(x)=-(x2-4)(x+1). It is known that for x intercept put y=f(x)=0 then solve…

Q: h(x)=ln(1/2 - x)

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

Q: The antiderivative of the function f(æ) 6. + 8x is. -6 + 16.0x? + c -6 4.0x? + c 6 + 4.0x² + c -6 +…

A: We have to find the antiderivative of the function f(x) = 6x2 + 8x

Q: Find f(4) using forward, backward and central difference of: (3 – 2x)2 f(x) = %3D x2 Step size = 02

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Q: Find f'(4) using forward, backward and central difference of: (3 – 2x)² | f(x) = x2 Step size = 0.2…

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Q: For the following exercises, find the critical points of the following generic functions. Are they…

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Q: Find f'(a) for -7 f(x) = V11 – 9a f'(a) = %3D

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

A: the given function is

Q: For y= 3x3 + 27x2 - 6x, determine concavity and the x values where points of inflection occur.  For…

A: Given:-  y= 3x3 + 27x2 - 6x To find:- concavity and the x values where points of inflection occur

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

A: The given function is, y=x2+4x+5

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

A: Given function  y=x2+x+6x-1 For Finding Extremum Point of Function 1. Evaluate ƒ at all critical…

Q: Assume the total revenue from the sale of x items is given by R(x) = 35 In (4x + 1), while the total…

A: Profit function, P(x)=R(x)-C(x)

Q: For the following exercises, consider a pizzeria that sell pizzas for a revenue of R(x) = ax and…

A: Given,           Rx=7x and Cx=160-2x+x2To find : How many pizzas sold maximizes the profit.

Q: For the following exercises, find the critical points of the following generic functions. Are they…

A: Given function : y=x-1a    where  a&gt;1 For finding the critical point we have to differentiate the…

Q: For the following exercises, use the vertex (h, k) and a point on the graph (x, y) to find the…

A: 46. h,k=-2,-1, x,y=-4,348. h,k=2,3, x,y=5,12

Q: The antiderivative of the function f(x) 6 + 8x is -8 + 3.0x2 + 6 + 4.0x2 + c 6 + 16.0x? + c -6 4.0x?…

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Q: Match the horizontal asymptote with its corresponding function. 5x+2 f(x) = 3x2 + 1 a. f(x)= 2x2+1…

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Q: For the following exercises, consider a pizzeria that sell pizzas for a revenue of R(x) = ax and…

A: This question can be solved using the concept of maxima and minima.

Q: A manufacturer of household items has total revenue given by the function R=18.5x and has total cost…

A: Draw the graph for R and C.

Q: The antiderivative of the function f(x) = .8 + 10x3 is. %3D

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Q: The total revenue in Php received from the sale of x units of children toy is given by R(x) = 3x² +…

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Q: 5) [ (x² +1)´dtan x3

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Q: Find the most general antiderivative of the function f(x) = 72° – 6x³ + 3x?.

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Q: find the maximum revenue for the function R(x)=356-0.9x^2

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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: Find (f-1)'(a) for f(x) = V3x + 4 when a = 2. (Enter an exact answer.)

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Q: An electronics manufacturer determines that the profit P(in dollars) obtained  by producing and…

A: Consider the given function, Px,y=8x+10y-11000x2+xy+y2-10,000 Noe find the critical points by…

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

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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.