x + 5 x < -2 y = 2.x –1 x 2 -2

Q: Determine where the graph of the function F(x) =x²-15x downward. Also, find all inflection points of…

A: We need to determine where the graph of the function f(x)=x3-15x is concave upward and where it is…

Q: Please can you explain if y = 1/4x 0 5 is a power function?

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Q: Determine where the function is concave upward and where it is concave downward. f(x) = (x – 5)2/3…

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Q: Suppose that function f cubes x and adds 20. Write an equation for f−1(x).

A: The given function is

Q: 2. 245 Y=-8Cos(lox+ 2) +4 (6x Is the function flipped across the X-axis? Explain why or why not

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Q: Sketch the graph of the following function: f(x)= -(x+3)^3 (x-1)(x-2)^2 Please write neatly…

A: Explanation of the answer is as follows

Q: Find the points of inflection and discuss the concavity of the graph of the function. f(x) = (6 −…

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Q: It is a fact that y(x) = 3x² – x + 1 is a function. Which y-value (output) does this function assign…

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Q: Estimate how much the function f (x) = 1/1 + x2 will change if x decreases from 1 to .9.

A: Given: The function  f(x) = 11+x2 To find: How much the given function will change if x decreases…

Q: (1 – x) 2

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Q: Graph the piece-wise defined function. for x -1

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Q: Describe the x-values at which the function is differe f(x) = (x + 2)2/3

A: To describe all possible x values at which the function is differentiable.

Q: What is the effect on the graph of the function f(x)= √1/2x when f(x) is replaced with f(x)+2,A,B,C,…

A: Substitute f(x)+2 in place of f(x).

Q: Without graphing, compare the graphs of the indicated functions from the given function. 3. f(x) =…

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Q: Find the points of inflection and discuss the concavity of the graph of the function. f(x) = (x −…

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Q: Find the points of inflection and discuss the concavity of the graph of the function.

A: Given function: f(x)=xx+3

Q: What is the range for the function h(x) = (x – 3)² + 2? -

A: Given : hx = x-32+2

Q: Find the points of inflection and discuss the concavity of the graph of the function.

A: Consider the function, fx=x-23x-1 To calculate the double derivatives of the given function,…

Q: Differentiate the function below. y=(x2+2)(x2-3)8   The answer is (2x)(x2-3)7(9x2+13) but I keep…

A: Given ,  y=(x2+2)(x2-3)8 Let   u=x2+2     and     v=(x2-3)8 Therefore ,y=uv differentiate with…

Q: determine where the graph of the function is concave upward and where it is concave downward. g(x)=…

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Q: Find the domain and range of the function without graphing f(x) = 2√x

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Q: How many points of inflection does the function (x)=x°+ x have?

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Q: Find the points of inflection and discuss the concavity of the graph of the function.

A: Given, f(x)=x+3x points follows f'(x)=0 is inflection point…

Q: Your friend claims that the graph of f (x) = (2x + 1)/x is the graph of f (x) = 1/x shifted 2 units…

A: Verify that the graph of  f1x=2x+1x is 2 units upward of the graph of  f2x=1x.  Simplify f1x=2x+1x.…

Q: Find the points on the graph of the function that are closest to the given point. f(x) = x² – 4,…

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Q: Determine the equation of the line tagent to the function f(x)=x(5-x)4 at x=3

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Q: Suppose that the revenue from selling x washingmachines isr(x) = 20,000(1 - 1/x)dollars. Use the…

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Q: I need to graph the function f(x+1) given the graph of f(x)=x^2

A: As we replace 'x' with 'x+1' in f(x). The given graph of f(x) will shift towards left i.e towards…

Q: Find the domain of the following function: h(x)=√(2x-3)(x+4) Be sure to write your answer in…

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Q: The Abdul family is comparing the costs of two different high-speed Internet services. With plan A,…

A: The cost of Plan A is given by  f(x)=50x+199 The cost of Plan B is given by  g(x)=90x+50 where x is…

Q: Find the point of the graph of the function that is closest to the given point: f(x) = 2x+9 ;…

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Q: For the function f(x) = 6 9", calculate the following function values: f( – 2) = () f f(0) %3|

A: the solution is given below

Q: What are the features of the function f (x) = 2 (})* – 1 graphed below?

A: The graph is:

Q: Find the slope of the graph of the function at the given value. f(x) = 4x+ 8. when x = 5 %3D

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Q: Differentiate the function. y = (4x-11)2

A: Chain Rule of differentiation : dydx=dydu·dudx

Q: Find the points of inflection and discuss the concavity of the graph of the function. f(x) = x√(9 −…

A: The function is given as x9−x In order to find the inflection point and concavity, second derivative…

Q: Find the points of inflection and discuss the concavity of the graph of the function. f(x) = (x +…

A: Our Aim is to find the points of inflection and discuss the concavity of the graph of the function…

Q: What are the features of the function f(x) 1 graphed below?

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Q: 1. Determine the domain of the function plotted below. y 6 -6 6 x

A: Domain is the set of x-values for which function is defined.

Q: Compared

A: We will find compare the graphs of the function.

Q: Determine the end (long run) behavior for the function below: f(x) = –2(x – 1)³(x+ 2)²

A: We first find the leading term of the given function  We will ignore the constants with the xs to…

Q: Find the point on the graph of the function that is closest to the given point: f(x)= 2x+8; (0,18)

A: We have given f(x)= 2x+8; (0,18)

Q: Without graphing, compare the graphs of the indicated functions from the given function. 3. f(x) = *…

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Q: Graph the Piecewise Function: x + 4, if 0 %D Click this Coordinate Plane to draw the Your answer:…

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Q: What is the domain of the function y = 3sin–1(2t)?   Can you explain how to think about the above…

A: The given function,

Q: х — 2 if x 2

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.