The function f(x) = 4ᴫx3/3 describes the volume, f(x), of a sphere of radius x inches. If the radius is changing, find the instantaneous rate of change of the volume with respect to the radius when the radius is 5 inches. Express the answer in terms of ᴫ .

Q: consider the equation f(x) = 2x2 - x find the average rate of change between x=3 and x=6

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Q: Find the instantaneous rate of change in f(x)= 3/x^2 at x=-2.

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Q: The approximate rate of change in height of a certain shrub in a nursery is given by f ' ( x ) = 12…

A: f'x=12x Integrating with respect to x on both sides, we get ∫f'x dx=∫12xdx⇒fx=12·lnx+C   →1…

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Q: The degree of the derivative of f(x) = (3–x)'(x – 12)° is

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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) = 5x2 describes the volume of a rectangular box, f(x), in cubic inches, whose…

A: Average rate of change is defined as change in quantity observed over a given interval of values.…

Q: Find the average rate of change of f (x) = -x+5x+1 from x=2 to x=7. Simplify your answer as much as…

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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: 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: 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: Find the average rate of change of f(x) 7x-8 on the interval 1, a. Your answer will be an expression…

A:

Q: Find the rate of change of the function f (x) = (x + 1)/(1 - 5x) with respect to x when x = 1.

A: The given function f(x) - f(x) = x+11-5xRate of change of function is given by ddxf(x) =…

Q: Find the average rate of change of f(x)=2x^2−3 on the interval [3,a] Your answer will be an…

A: We have the given function as f(x)=2x2−3   We have to find the average rate of change of f(x) on…

Q: What is the instantaneous rate of change of f(x) = 3x + 5 at xo 1?

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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: 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 – 8x+8, determine the average rate of change of the function over the…

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Q: if f(x)=17x^2-x^3   , what is the rate of change of f’(x) at (-1,18)?

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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: Find the derivative. g(x) = (4x – 2)° – Vr + 8

A:

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: Find the second derivative of the function.

A: Given: f(x)=x2+3xx-4 To find f''

Q: Suppose the value of yy and the value of xx vary together at a constant rate of change (so that…

A: 1.The value of y and x vary together at a constant rate of change and the value of y = 1.5 and x =…

Q: The function f(x) = πx2 describes the area of a circle, f(x), in square inches, whose radius…

A: Given,  The area of the circle is described by the function  fx=πx2 in square inches. Where x is the…

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: 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: 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) = 7x² – 4 on the interval (3, b]. Your answer will be an…

A: Finding the average rate of a function in a given interval

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…

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Q: Find the average rate of change of f(x) = 4x² – 7 on the interval [1, 6]. Your answer will be an…

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 of f(x)=4x^2-2 from 2 to 4 

A: For the function f(x) the rate of change in a closed interval a to b is given (f(b)-f(a))/b-a Here,…

Q: 33. Solve for the second-order derivative of the function below. Y = x 3x3 За

A: Differentiate two times wrt x

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A: Differentiating f(x) with respect to x by dividing rule

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: The function f(x) = 4ᴫx2 describes the surface area, f(x), of a sphere of radius x inches. If the…

A: Given: The surface area of a sphere is, fx=4πx2 . Radius of the sphere is, x=6 inches. The…

Q: find the instantaneous rate of change for the funtion at the given value g(x)=x+11x-15 at x=1

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Q: Find the average rate of change of f(x)=9x2−8 on the interval [4,b]. Your answer will be an…

A: Given function , f(x)=9x2-8 on the interval 4,bThe average rate of change of fx=9x2-8 is in…

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 the function f(x) - 3x – 2x – 2, on the interval 2 < x < 4.…

A: NOTE: Refresh your page if you can't see any equations. . take x=2

Q: find the average rate of change for f(x)= 3x2-x+5 from x=2 to x=2+h in simplified form

A: Given function:

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…

Exponential Growth Model

The relation that represents an exponential function is: