The function f(x) = 5x2 describes the volume of a rectangular box, f(x), in cubic inches, whose square base has sides that each measure x inches and whose height is 5 inches. If x is changing, a. Find the average rate of change of the volume with respect to x as x changes from 2 inches to 2.1 inches and from 2 inches to 2.01 inches. b. Find the instantaneous rate of change of the volume with respect to x at the moment when x = 2 inches.

Q: Given the function h(x) = –x² – 6x + 17, determine the average rate of change of the function over…

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

A: The given function is f ( x ) = 3x2 – x and x1 = 2 , x2 = 4. In order to find the average rate of…

Q: For the function y=x2,compute the average rate of change between x=9 and x=10

A: We have to find the average rate of change of function.

Q: The function f(x) = (4/3) πx3 describes the volume, f(x), of a sphere of radius x inches. If the…

A: fx=43πx3 Differentiating with respect to x, we get f'x=ddx43πx3=43π·3x2            ∵dxndx=nxn-1=4πx2

Q: Find the instantaneous rate of change of the function at the given value f(x)=6x2-4x+3; x=2

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Q: The function f(x) = x3 describes the volume of a cube, f(x), in cubic inches, whose length, width,…

A: Given volume function fx=x3 to find instantaneous rate of change of the volume x=4 in

Q: Given the function h(x) = x^2 + 10x * 21, determine the average rate of change of the function over…

A: Given function h(x)=x2+10x+21       , -10 <x<-3

Q: Find the average rate of change of f (x)=-x+3x+6 from x=2 to x=6. Simplify your answer as much as…

A: Given:- f(x) = -x2 +3x+6  To find:- Average rate of change of given function from x=2 to x=6

Q: Find the average rate of change of f(x) = 3x2 - 5 from x1 = 6 to x2 = 10.

A:

Q: The function f(x) = x2 describes the area of a square, f(x), in square inches, whose sides each…

A: Given function fx=x2 To find rate of change of area.

Q: For the given function, find the instantaneous rate of change at x= 4 Y=(x^2-2) (x^2 -6x +6)

A: For this problem, we have find derivate of given function at one time. And later substitute value of…

Q: Given the function h(x) = x² + 2x – 2, determine the average rate of change of the function over the…

A: Now, we are given the function : h(x)=x2+2x-2 Average rate of change of a given function f(x) over a…

Q: find the average rate of change of the function from x=1 to x=2  f(x) = -(2/x^2)   average rate…

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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: Given f(x)= x^2+4x, find the average rate of change of f(x) on the interval [-2, -2+h]

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Q: The function f(x) = ᴫx2 describes the area of a circle, f(x), in square inches, whose radius…

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: The function f(x) = x3 describes the volume of a cube, f(x), in cubic inches, whose length, width,…

A: Given: fx=x3,  x=5 inches

Q: For function f(x) = 2" , state a) the average rate of change from x =1 to x=5 b) the instantaneous…

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Q: Given the function h(x) = x² + 10x + 21, determine the average rate of change of the function over…

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Q: Given the function h(x) = x² – 7x + 6, determine the average rate of change of the function over the…

A: The rate of change of a function is given by it's derivative.

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

A: The instantaneous rate of change of a function at a point can be evaluated first by finding the…

Q: Given the function h(x) = x2 + 10x + 21, determine the average rate of change of the function over…

A: The objective is to determine the average rate of change of the given function.

Q: Consider the function f(x) = -3x²³ +3x²-3x -\ Find average rate of change on interval (-4,-1). Find…

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Q: Find the average rate of change of f(x) = x-4x+2 from x = 2 to x = 5. Simplify your answer as much…

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Q: find the average rate of change f(x)=8x^2-2 on the interval [5,a]

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Q: Find the average rate of change of f (x) =-2x´+6 from x=-3 to x=-1. Simplify your answer as much as…

A: Topic  = Algebra

Q: when you have f(x) = x^2 + 7x +10 / x^2 - 7x +6 what is the average rate of change of the function…

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Q: What is the average rate of change for the function f(x)=x3−6x2+4x+7f over the interval 0≤x≤5?

A: We have to find

Q: Find the rate of change of the function f(x) = x + 2/1 − 8x with respect to x when x = 1.

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Q: Find the relative rate of change and evaluate at the given function

A: To find the relative rate of change we have to find f ' (x) [first derivative of f(x)]

Q: Given f(x) + 4x + 2, find the average rate of change on the interval [1, 3].

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Q: Find the average rate of change of f(x) = 3x2 - 2, from 2 to 4.

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Q: Find the instantaneous rate of change for the function: f (x)= 4x = 2x²- 5

A: The instantaneous rate of change of function will be find by differentiate the function with respect…

Q: Given the function f(x) = –x² – 5x + 12, determine the average rate of change of the function over…

A:

Q: Determine the value of k so that the rate of change of the function f (x) = 4x² + kx – 7 is 7 when…

A: Answer

Q: Find the average rate of change for the function between the given values. 18) f(x) = 4x2; from 0 to

A: The average rate of change of a function f(x) on the interval [a, b] is fb-fab-a. The given function…

Q: The function f(x) = ᴫx2 describes the area of a circle, f(x), in square inches, whose radius…

A: Consider the function that describes the area of a circle  fx=πx2

Q: Given the function f(x) = -x² – 7x + 19, determine the average rate of change of the function over…

A: Given function is: fx=-x2-7x+19 And the given interval is: -9≤x≤3 At x=-9:…

Q: Find the average rate of change of the function f(x) 2x^2−4x +1 from x = 1 to x = 5. Average rate…

A: The given function is fx=2x2-4x+1. The average of rate of change of the function f from x=a to x=b…

Q: Given the function f(x) = -x²+ 3x + 8, determine the average rate of change of the function over the…

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Q: Find the average rate of change of f (x) = 2x- 8x from x= 2 to x = 5. Simplify your answer as much…

A: We will find the average rate of change.

Q: Given the function f(x) = -x² – 7x + 15, determine the average rate of change of the function over…

A: Given, fx=-x2-7x+15 over the interval -9≤x≤3 To find the average rate of change.

Q: The function f(x) = 5ᴫx2 describes the volume, f(x), of a right circular cylinder of height 5 feet…

A: Given that, Volume of right circular cylinder whose height is 5 feet and radius is x feet is,…

Q: Find the average rate of change of g(x) = 7x* + 6. on the interval [-3, 3].

A: This question can be solved by calculating the value of function at x=-3 and x=3

Q: find the average rate of change of f(x) = -x3+3x2 from x=-1 to x=4

A:

Q: Given the function h(x) = -x² – 6x + 11, determine the average rate of change of the function bver…

A: The average rate of change of a function, y=f(x) over the interval, a, b is calculated using the…

Q: Calculate the instantaneous rate of change for the function f(x)=2/3x+5 when x=-7

A: The function is f(x) = 2/(3x + 5). We have to calculate the instantaneous rate of change for this…

Q: Given the function g(x) = -x2 – 3x +5, determine the average rate of change of the function over the…

A:

Exponential Growth Model

The relation that represents an exponential function is: