Determine the open intervals on which the function is increasing, decreasing, or constant. (Enter your answers using interval notation. If an answer does not exist, enter DNE.) 3x + 2, x² - 2, xs -1 x > -1 f(x) =

Q: 1 Let f(x)= 4x² + 2 An equation of the line L tangent to the graph of f at the point ( ,) is (fill…

A: Given: ------------------------------------------------------------------------------ To find: An…

Q: Let f (x) = x3 – 3x2 – 1, x 2 2. Find the value of df-1 at the point x = -1 = f (3). dx -

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Q: Find the extreme values of the function f on the interval [-5, 13]. If an extreme value does not…

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Q: Find the function f (x) for which f (x) = e-5x, f (0) = 1.

A: A function is a relation which maps each value in its domain to exactly one value in its range. For…

Q: Use your calculator to make the graph of f(x) = x³ - 5x. df (a) Is- positive or negative at x = 2?…

A: The given function is f(x)=x3-5x

Q: Determine if the given function below is continuous at x-2. Attached your complete solution and…

A: Topic = Continuity

Q: -x/18 flx)= xe [-2.6

A: It is absolute maximum and minimum problem.

Q: Find the values at which the transition points occur, if any, of the function. - 2x + 8 1 f(x) -…

A: Find transition point

Q: Determine whether or not the graph of f(r) = 3(x – 5)4/5 has a vertical tangent or vertical cusp at…

A: Given: Let's determine whether or not the given graph has a vertical tangent at x=5. The correct…

Q: If f(5) = 13, f 'is continuous, and f '(x) dx = 17, what is the value of f(7)? %3D f(7) =

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Q: X +7 At what points is the function y= continuous? 2 x - 13x + 42 X

A: NOTE: Refresh your page if you can't see any equations. . to find the undefined points, take…

Q: x+3 10. At which points do the functions y = fail to be continuous? If any, are x2-3x-10 the…

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Q: the interval in which the root exists for the function f(x) =x² – 16=D0 is O a. [0,3] O b. none O c.…

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Q: (b) Given f(x)=9x – 6x² + x. Find F(x) dx in the form a In|g(x) + h(x)], where a is a constant

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Q: find the derivative:  c(x)=(x2)500x (the choices are in the image bellow)

A: This question is based on Chain rule differentiation. d/dx {f(x).g(x)} = g(x).d/dx{f(x)} +…

Q: Find a, b, and c for the function f(x) = a sin(bx – c) such that the graph of f matches the figure.…

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Q: 78. For what values of x does the graph of f (a) = x³ + 3x? + x + 3 have a horizontal tangent? %3D…

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Q: Find the interval on which f(x)%= -X xe is increasing. a. (-00,1] b. (-0,2] c.(-0,3] d. [1.2]

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Q: For what value(s) of x is f(x) = 3?

A: given :  f ( x ) = 3  find value(s) of x = ?

Q: Find the absolute extrema of the function (if any exist) on each interval. (If an answer does not…

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Q: 2. Suppose f(x+3)%3D f(xr), what is the period of the function f ? (A) 4 (B) 3 (C) 2 (D) 1

A: topic - functions

Q: Which of the following is the x-coordinate of a relative extremum of the function f(x) = = Arct…

A: We will use first derivative test to determine the extremum of the function.

Q: Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an…

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Q: 2. Given the function f (x) = sinx and g(x) = x², find the value of g(fG)

A: Given function are f(x) = sin x   and g(x) = x2 We have to find the value gfπ4

Q: find and sketch the domain for each function ƒ(x, y) = ln (xy + x - y - 1)

A: Given- fx,y=lnxy+x-y-1 To find- The domain and sketch the graph of above function. Concept Used- We…

Q: Let a be a real valued constant. Find the value of , 5¤ |x| dx. 50a O It does not exist. 50

A: Consider the given integral. ∫-425αxdx The objective of the problem is to evaluate the given…

Q: The hypotenuse of an isoscles right triangle is to be made into a circle C. Express the area A of C…

A: Given that: The hypotenuse of a right isosceles triangle is made into a circle C.Length of legs of…

Q: Determine where the function is concave upward and where it is concave downward. (Enter your answer…

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Q: Consider the equation below. (If an answer does not exist, enter DNE.) f(x) = x4 - 8x2 + 8 %3D (a)…

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Q: Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an…

A: Given ,  f(x) = 2x + 8 We have to find critical point of f(x)  To find , critical point…

Q: Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an…

A: f(x)= 3x^4+8x^3-18x^2 f'(x)= 12x^3+24x^2-36x f'(x)= 0 12x^3+24x^2-36x=0 12x(x^2+2x-3) x=0,-3,1

Q: Find the absolute extrema of the function (if any exist) on each interval. (If an answer does not…

A: Function: f(x) = x2 – 6x   The condition for the absolute extreme of the function is,   Solve the…

Q: Q6: Find the absolute maxima and absolute minima For the function f(x) =sinx 0 < x < 2n

A: To find the absolute maxima and absolute minima, first, we have to find all the critical points of…

Q: x+1 At what points is the function y = continuous? x2 - 6x + 5

A: To solve this problem we will use the concept of continuity of rational function.

Q: Let f(x) = x² – 4x – 5, x > 2. Find the value of df-1/dx at the point x = 0 = f(5).

A: (f-1(x))' = df-1dx = 1f'(f-1(x))

Q: Please

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Q: mat ftoydk = hat f(x)dx: 1 Find the 2 a

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Q: Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an…

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Q: X + 1 At what points is the function y = continuous? x2 - 10x + 9

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Q: x+6 At what points is the function y = continuous? x-14x+48

A: If function f(x) is said to be continuous at x= a if f(x) is defined at x=a. limx→af(x) exist i.e,…

Q: Find the absolute extrema of fGx\=x. %½x°- 2 x+1 on the interval E1,2I.

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Q: (x) is an even function, and if f 6 f(x) dx = 15, find f³, f(x) dx.

A: Given query is to find the value of the Indicated integral.

Q: Give the increasing and decreasing intervals and relative extrema    f(x)=e^(-2x^2+x)

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Q: What is the period of the function? Ay 2 3t 4 5 6 7 8 9 0n -1 -2 -3 -5 5432

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Q: 1 + y =

A: To solve the following problem, we use the concept of seperation of variable, then integrate both…

Q: Consider the function f (x) = 0+3 As the values for x continue to increase to positive infinity,…

A: Given: f(x)=xx+3

Q: If f(5) = 14, f' is continuous, and f '(x) dx 20, what is the value of f(7)? %3D f(7) =

A: Consider the given integral is, I=∫57f'(x)20=f(x)5720=f(7)-f(5)f(7)=20+f(5)f(7)=20+14f(7)=34

Q: According to a mathematical model of coughing, the velocity v, of the airstream is related to the…

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Q: The function f, shown below, is comprised of a semi-circle and piecewise linear segments. What is…

A: Since the function f is comprised of a semi circle  and piece wise linear segments.  Therefore it…

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.