An efficiency study of the morning shift at a certain factory indicates that an average worker arriving on the job at 7:00 A.M.will have assembled f (x) = x3 + 6x2 + 15x units x hours later.Approximately how many units will the worker assemble between 8:00 and 8:15 A.M.?

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Q: s rate of change of the function at the given x-value. f(x) = 3x2 + x − 3 at x = 1

A: Given: fx=3x2+x-3 To find rate of change of f(x) at x=1

Q: Find the length L of the graph of 3 ( a) f(x)=x/2 +1 for 0<x< 4

A: Since you have asked multiple questions in single request.so we will answering only first question.

Q: Find the domain of the function. f(x) = ln ( 1/ (x + 1)

A: f(x)=ln1x+1

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Q: Find the domain of the function. f(x) = ln(x^2 + 1)

A: Definition used:The domain of a function is the complete set of possible values of the independent…

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Q: Find the average rate of change of f(x)= 3x^2-2x+6 from x1=4 to x2=7

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Q: The graph of f (x) = |x| is reflected over the x-axis, shifted vertically up 1 unit, horizontally 3…

A: This question is based on transformation of graph.

Q: Suppose f(x)=6x2+9x−14f. Write an expression in terms of x and h that represents the average rate of…

A: fx=6x2+9x-14

Q: It was determined that the number of prey consumed by a predator over a period of time was a…

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Q: Suppose a company wants to introduce a new machine that will produce a rate of annual savings​ (in…

A: given S'x=150-x2C'x=x2+114x where S'x is the rate of annual saving and C'x is the rate of annual…

Q: An efficiency study of the morning shift at a factory indicates that an average worker arriving on…

A:

Q: Let f(x) = -x² - 4x + 11. What is the average rate of change from x = -5 to x = 2? %3! O-7

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Q: Find f" (1) when f(x) = x² − 3x³ + 2x² +10. Round your answer to three decimal places, if necessary.

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Q: Suppose f(x)=6x2+9x−13. Write an expression in terms of x and h that represents the average rate of…

A: Average rate of change is ratio of change in function values and time interval.

Q: Differentiate the following function. f(x) = e - 2x2 - 4x d (e -2x2 - 4x) - 2² - *x) = [ dx

A: Given f(x)=e(-2x^2-4x)

Q: Differentiate. f(x) = - 2 e -X t'(x) = ]

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Q: When a certain drug is taken orally, the concentration of the drug in the patient's bloodstream…

A: The concentration of the drug in the patient's bloodstream after t minutes is given by

Q: Let L(x) be the linearization of the cube root function at x=8. When using L(x) to approximate the…

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Q: 1. Given the function f(x) = Vx5 – 3Vx², find the interval(s) of increase.

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Q: Determine the extreme values of the ff. functions. f(x) = x^2 + 3 on [1,3]

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Q: 9. Find the point of diminishing returns (x, y) for the function R(x) = 11,000 – x + 42x² + 800x,…

A: We have to identify the point of diminishing return for the input-output function. For each…

Q: Find the inflection points of the function f(x) = ln(x^2 + 1)

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Q: An article† in The New York Times states, "The number of gas stations [in a city] grows only in…

A: Part (a) G1=cN10.77G2=cN20.77N2=2N1G2=c2N10.77G2=c20.77N10.77G2=20.77G1G2=1.705G1G2≈1.71G1 If one…

Q: If x is large, which function grows faster, f(x) g(x) = x2? %3D

A: The given function is fx=2x   and  gx=x2

Q: During a flu epidemic, the total number of students on a state university campus who had contracted…

A: "Hey, since there are multiple subparts posted, we will answer first three subparts. If you want any…

Q: f(x) = x^3 -1000x +2022 How many local minima does this function have? are inflection points of…

A: Given function f(x)=x3-1000x+2022

Q: Suppose f(x)=5x2+8x−16. Write an expression in terms of x and h that represents the average rate of…

A: Average rate of change is ratio of change in value of f(x) and change in x.

Q: 3. Armaan claims that the functions f(x) = 32x + 5 and g(x) = 32* + 8 have different instantaneous…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Suppose f(x)=6x2+9x−12. Write an expression in terms of x and h that represents the average rate of…

A: The average rate of change is given by: f(x+h)-f(x)h

Q: Suppose f(x)=−x2+10x−6 models the per household smoothie consumption, in quarts, in the town of…

A: Given that : fx=-x2+10x-6. Therefore, take first order derivative : f'x=-2x+10. At f'(x)=0 , we get…

Q: The daily cost of producing x high performance wheels for racing is given by the following function,…

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Q: A pharmacologist studying a drug that has been developed to lower blood pressure determines…

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Q: Find f' (æ) for f (x) = 7 ln(4 + æ²).

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Q: If x is large, which function grows faster, f(x) = 2x or g(x) = x2 ?

A: Given,            fx=2x or gx=x2To find : if x is large, then which function grows faster.

Q: A company has found that its rate of expenditure​ (in hundreds of​ dollars) on a certain type of job…

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Q: Find f''(x) for: f(x)=ln⁡x/4x

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Q: At what value of x does the local max of f(x) occur?

A: Given, fx=∫0xt2-491+cos2tdt

Q: Given f(x)=ln(5x), what is f'(x) when x=14.2?

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Q: What is the meaning of g(f(0)) in the context of the virus epidemic?

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Q: Find the absolute extreme values of the function on the interval. f(x)=ln(x+2)+1/x , 1 less than or…

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Q: Given a total-revenue function R(x) = 900/x -0.1x and a total-cost function C(x) = 1400 (x +2) +800,…

A: Given, Total revenue function Rx=900x2-0.1x Total cost function Cx=1400x2+213+800 We have to find…

Q: 2. Determine the zeroes of 2 x² = x f(x) instantaneous zeroes using a table of values. — 3x 4 and…

A: To find the zeroes of the polynomial.

Q: An article† in The New York Times states, "The number of gas stations [in a city] grows only in…

A: It is give that population is N and G be the number of gas stations in a city related by G=cN0.77.…

Q: Let L(x) be the linearization of the cube root function at x=64. When using L(x) to approximate the…

A: The linearization L(x) for tge function f(x) at x =a is given as L(x) = f'(a) (x-a) + f(a)

Q: Find the average rate of change of f (x) = -3x+3 from x =-4 to x= -2. Simplify your answer as much…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.