Mr. dela Cruz encourages his students to solve math problems fast and with accuracy. He observed in his math class that the time it takes a student to solve x word problems is defined by the function f(x)= 3x2-x where f(x) is in minutes. Find the average rate of change in solving time from 3 to 5-word problems.

Q: Find the second derivative of the function. f(x) = 4x3/2

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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: A company's revenue from selling x units of an item is given as R = 1600x - x. If sales are…

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Q: Find the points of inflection given the function: Given the function f(x) = 2x³+ 3x²-12x-9 Where…

A: For the inflection point, second derivative is equal to zero.

Q: What is the slope of the line tangent to the graph of f (x) = 2x2e" at x = -2? Express your answer…

A:

Q: Find the average rate of change of f(x) = 3x² – 9 on the interval [3, a]. Your answer will be an…

A: The average rate of change of function over an interval [a,b] is given by  f(b)-f(a)b-a

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

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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: f (x) = 3 · 5" + e 4x²+7¤

A: We have to find derivative

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: 2х + 1 f(x) : х+ 2

A: Given:…

Q: What is the slope of the graph of f (x) = x3 - 4x2 + 6 at x = 2? Write the equation of the line…

A: Given :        The function f(x) = x3 - 4x2 + 6    To find the slope of the graph f(x) = x3 - 4x2 +…

Q: Find the equation of the line tangent to the graph of f(x)= (lnx)3  at x=10.

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

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Q: An accessories company finds that the cost, in dollars, of producing x belts is given by C(x) = 780…

A: Given :  Cost function :  C ( x ) = 780 + 35 x - 0.063x2  Find the rate at which average cost is…

Q: Find the equation of the line that is tangent to the graph of f(x)=(3x+1)/(4x-3) at the point where…

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

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Q: Mr. dela Cruz encourages his students to solve math problems fast and with accuracy. He observed in…

A: Given- Mr. dela Cruz encourages his students to solve math problems fast and with accuracy. He…

Q: What is the average rate of change of f (x) from x1 = -3 to x2 = 1? Please write your answer as an…

A: Question is solved.

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: Find the average rate of change for f(x)=x^2-3x-10 from x=4 to x=6.

A: Use average rate concept

Q: Find the average rate of change of g(x) = 4x² + 4 on the interval [-4, 3]

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Q: Find the average rate of change of g(x) = 5x³ + 4 from x = - 4 to x = 4.

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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 of f(x) = 8x² − 4 on the interval [5, a]. Your answer will be an…

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Q: What is the rate of change of the function f(x)=−7

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Q: The function f(æ) can be approximated by L(x) = 3 – 2(x – 4), near x = 4. What is the value of f'…

A: topic -linear approximation

Q: Find the function with the given derivative whose graph passes through point P f'(x)=1/4x3/4,…

A: To find the function with the given derivative that passes through the point (1,-2).The derivative…

Q: Find the average rate of change off(x) = 3x-3x-2 from x = 1 tox= 3. Simplify your answer as much as…

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Q: (2x³ – 5)(3x² +1) f(x)= x +7

A: Derivative problem.....

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: 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…

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Q: If (x) = -4x – 3, find the average rate of change on the interval [0,2].

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Q: What is the average rate of change of f(x) from x = -5 to x2 = 1? Please write your answer as an…

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Q: Find the average rate of change of f (x)= 2x-9 from x 7 to x= 10. Simplify your answer as much as…

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Q: On the basis of data for the years 1911 through 1991, the expected life span of people in a country…

A: First find the number of years x from 1908 to date of birth of the person 1966 than put that x in…

Q: What is the average rate of change of f(x) from x1 = -0.2 to x2 = 7.8? Please write your answer…

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Q: The derivative of 4.x5 is f(x) f(x) = Зх-2

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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 average rate of change of f(x)=2x²+3x-1 from 1 to 2. -9 18 3

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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: Suppose that the total profit in hundreds of dollars from selling x items is given by…

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

Q: Find the equation of the line tangent to the graph of f(x)= x2 over (3x-4)3 at the point…

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Q: What is the average rate of change of f(x) from x₁ = -8.2 to x₂ = 2.8? Please write your answer…

A: Follow the procedure given below.

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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Q: Use the definition of the derivative to solve.

A: To determine the derivative of the 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…

Q: The average annual pay for truckers P in a certain country​ (in thousands of​ dollars) can be…

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Q: Find the second derivative of the function f(x) = 5(2 − 7x)4

A: Find the first derivative as shown below: f'x=ddx52-7x4        =42-7x3ddx2-7x        =5· 42-7x3-7…

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.