The function f(x) = x3 describes the volume of a cube, f(x), in cubic inches, whose length, width, and height each measure x inches. If x is changing, Solve, the average rate of change of the volume with respect to x as x changes from 4 inches to 4.1 inches and from 4 inches to 4.01 inches.

Q: Find the derivative.   g(x) = 4^x/x^4

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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 function is fx=x3

Q: Find the derivative of the function. f(x) = ((x2 + 3)5 + x)2

A: We use the power rule and chain rule.

Q: The function f(x) = 4ᴫx3/3 describes the volume, f(x), of a sphere of radius x inches. If the radius…

A: f(x) = 4πx33 Volume of sphere , f(x) = 4πx33 where,  x is the radius of sphere in inches.…

Q: Find an equation of the line tangent to the graph of f(x) when x = 2: f(x) = Vx+2

A: Find the equation of line

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

A:

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

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Q: Given the function g(x) = -x² – 5x + 8, determine the average rate of change of the function over…

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

A: Given: fx=x2. Here, fx describes the area of a square in square in inches

Q: Find an equation of the line tangent to the graph of f(x) when x = 2: f(x) = Vx +2

A:

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…

A:

Q: Find the average rate of change of f(x) = x3 - 5x2 + 27from - 3 to 2.

A: We know that, for the average rate of change, we divide the change in the output value by the change…

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 derivative of the function. F(x) = (x* + 3x² – 2)*

A: Use chain rule to find derivative of given function as shown in step 2

Q: Find the second derivative of the function.

A: Given function is  fx=4x32 The derivative used here is  dxndx=nxn-1 The derivative of the first…

Q: Find the slope of the line tangent to the graph of each function at the given point. f(x) = x3 - 2x;…

A:

Q: The average rate of change of the linear function f(x) =3x +5 between any two points is_________ .

A: Given that: The linear function f(x) = 3x + 5.

Q: What is the rate of change of the function y = - 2x – 1?

A: The rate of change

Q: The us population can be modeled by the function y=165.6x^1.345 where y is in thousands and x is the…

A: The US population is modeled by the function, y=165.6x1.345 where y is in thousands and x is the…

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

A:

Q: Find the slope of the secant line between x=−1 and x=2 on the graph of the function f(x)=−2x3 +3.

A: Given lines are x = –1 and x = 2. Given function is

Q: Given the function g(x) =- + 6x + 12, determine the average rate of change of the function over the…

A: Giveng(x)= -x2+6x+12    and -3≤x≤5

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: 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 of g(x) = 4x² + 4 on the interval [-4, 3]

A:

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…

A:

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: Write the equation of the line tangent to the graph of f(x) = -3x² + 5x +1 at x=1 and use it to…

A:

Q: Find the slope of the secant line between x=−3 and x=4 on the graph of the function f(x)=3x2−x+2.

A: we will find slope of secant line by two point slope formula

Q: Find the derivative of the function. f(x) =  x3 − 4 x2 + 2

A:

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: 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: The average number of vehicles waiting in a line to enter a parking ramp can be modeled by the…

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

Q: Find an equation of the line tangent to the graph of f(x) at the point (5,9): f(x) = e-3x-1o + 8

A:

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: b) Find and simplify the derivative of the function below: y = x°(3x² + 1)*

A: Use the chain rule and power rule of derivative and simplify the result.

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 derivative of the function. f(x) = x2 + 5 − 3x−2

A: Known fact: ddxxn=nxn-1ddxf±g=dfdx±dgdxddxk=0   where k is constant

Q: Find the derivative of the function. F(x) = (xª + 7x² – 3)4

A:

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

A:

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…