What is the closest value to the instantaneous rate of change of the following function at x = 2? f(x) = x³ - 2x2 – 5x + 1 %3D 01 O3 O-3 O-1

Q: Estimate the instantaneous rate of change at x= 1 for Ax) = /x + 1. a) -2 b) -0.5 c) 0.5 d) 2

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Q: Suppose x and y are functions of third variable t. In the equation x2+y2=45, what are the values of…

A: In the question it is given that x and y are the function of the variable t in the equation…

Q: A rectangle has width w inches and height h inches, where the width is twice the height. Both w and…

A: It is given that, a rectangle has width w inches and height h inches, where the width is twice the…

Q: Estimate the instantaneous rate of change of the function at x = -2. 2 (2, 0) -4 4 -2 -4 (-3, –5) a)…

A: Given:

Q: For which function is the instantaneous rate of change closest to 5 at x = 2? Ax) = x g(x) = x² + 1…

A: Consider the given information: To find the instantaneous rate of change closest to 5 at x=2.

Q: 5. Find the instantaneous rate of change of 1 g(x) = 2x – 32x° + 17x² – 9x + 4 at x = 2

A: Given equation is, gx=2x4-32x3+17x2-9x+4

Q: second. At what rate x changing when x = . O-16 O 16 8 O-8 in such way that the y-value increases at…

A: The given equation is;  y=x3-2x2+x-1.

Q: The projected population of a certain ethnic group(in millions) can be approximated by p(t) =…

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Q: We are given f(x) = 9x2 and f '(x) = 18x. Find the instantaneous rate of change of f(x) at x = 2.

A: Given function is

Q: Find the rate of change of x with respect to p. 4 x2 0 0.000001x2 + 0.09x + 5 dx dp ||

A: Proceed as shown below

Q: Given the function f(x)=x2/3, which of the following is a valid formula for the instantaneous rate…

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Q: In the equation, x2 +y² = 45, what is the value of the rate of change in y with respect to time t…

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Q: Given the g(x) function, what is the best estimate for the instantaneous rate of change at x=3? g(x)…

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Q: In the equation, x² +y² = 45, what is the value of the rate of change in y with respect to time t…

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Q: If f(x) = 3x + 2x + 6, find the instantaneous rate of change of f(x) at x = 1. -

A: Topic - applications of derivativea Instantaneous Rate of change of f(x) at x is given by slope of…

Q: Given the function f(x) = x2/3, which of the following is a valid formula for the instantaneous rate…

A: fx=x23fx+h=x+h23At x=8f8+h=8+h23f8=823=23×23=4

Q: 3. fox =V X at X T6

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Q: If f(x)=9x+6, find the instantaneous rate of change of f(x) at x=-5

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Q: Solve the problem. Compute the instantaneous rate of change of the function at at x = a. f(x) = -8x2…

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Q: Given a function f(x)=e2x−ex+1, what is the correct form of the relative rate of change R?

A: Given: The function is given by f(x)=e2x-ex+1   To determine:  The correct form of the relative rate…

Q: Find the instantaneous rate of change for the function at the given value. g(t) = 4 – t² at t = - 6

A: Consider the function fx=x2+4x We have to find the instantaneous rate of change for the function…

Q: ズ-1 f(x)- X + 3

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Q: S Зх-7 dx 10х2+3x+11

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Q: Determine the instantaneous rate of change at x = 3 for g(x) = x² − 2x+5. A. 2 B. 4 C. 6 D. 8

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Q: The number of bacteria in a culture is given by the function n(t)=960e0.4tn(t)=960e0.4t where tt is…

A: To find- relative rate of growth of this bacterium population

Q: Suppose a quantity described by the function y(t) = y0ekt, where t is measured in years, has a…

A: yt=y0ekt The quantity has a doubling time of 20 years. That is, yt=2y0 when t=20.

Q: 2. Find the instantaneous rate of change for y= arctan- at x = 3. 2 12 A. 85 2 В. 13 3n D. 4 С. О

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Q: 3. Determine the x-value(s) for which the function g(x) = In|x² +3x| has an instantaneous rate of…

A: Given function is Differentiating both sides with respect to x, we get

Q: Estimate the instantaneous rate of change given the following: f(x) =5 at the point (-3, — 2/1) x+5…

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Q: 1 What is the instantaneous rate of change of Y at x = 2? O -1 none of these -1 1 3 4

A: Given : y = 1/x

Q: As x increases, what happens to the instantaneous rate of change at (x,f(x)) for y-log(x) Z 13 4 5 6…

A: Since you have asked multiple questions here, we will solve the first question for you. To get the…

Q: Determine the instantaneous rate of change of the function y = 5x + 2x² 1 with respect to x at x-4.…

A: Find instantaneous rate of change

Q: 1. Given the following graph, determine: a) The average rate of change between -5sxs-3 b) The…

A: The average rate of change formula is y2-y1x2-x1

Q: Use Definition 1 or 2 to find the instantaneous rate of change of the function at the given value.…

A: The instantaneous rate of the function N(x)=1x, x=8

Q: If g'(x) is the rate of growth of a giant redwood tree in feet per year, what does (see picture)…

A: solution is given below

Q: Find the instantaneous rate of change for the function at the given value. F(x) = x2 + 3x at x = 8…

A: Given that Fx=x2+3x We have to find the instantaneous rate of change for the given function at x=8…

Q: If the rate of change in life expectancy I at birth for persons born in the United States can be…

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Q: | 10. For what value of c is the instantaneous rate of change for the function f(x) = 2\x equal to…

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Q: If g(x) = 3x3 + 6x2 + 4. What is the value ofthe instantaneous rate of change of g(x) when x = -1?

A: We have to solve the problem

Q: In some chemical reactions,the rate at which the amount of a substance changes with time…

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Q: The number of bacteria in a culture is given by the function n(t)=960e0.4tn(t)=960e0.4t where tt is…

A: Exponential Population model

Q: Find average rate of change for the function f(x) = /2x over the given interval if x changes from 2…

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Q: ズ-1 f(x) = X + 3

A: given: f(x)=(x-1)/(x+3) x=4 delta(x)=8

Q: find the instantaneous rate of change of the function at the given x-value. f(x)=x2 + 3x at x=4

A: f(x)= x2+3x  and x=4

Q: Suppose x and y are functions of third variable t. In the equation x2+y2=45, what are the values of…

A:

Q: Find the rate of change of x with respect to p. p= 9/ 0.000004x2 + 0.05x + 8 ,  x ≥ 0

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Q: Given the function g(x)=x² −2x³ +1, a. Estimate the instantaneous rate of change at x = 1. b. Will…

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Q: Given the function f(x) = x which of the following is a valid formula for the instantaneous rate of…

A: The given function fx=x23 The instantaneous rate of change is given by limh→0fa+h-fah

Exponential Growth Model

The relation that represents an exponential function is: