A function is given.  f(t) = 3t^2; t=2, t=2+h (a) Determine the net change between the given values of the variable. (b) Determine the average rate of change between the given values of the variable.

Q: Find the average rate of change of the function on the interval specified. h(x) = 3 − 6x2  on  [−2,…

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Q: A solid steel shaft at room temperature of 27°C is needed to be contracted so that it can be shrunk…

A: Given that, dθdt=-5.33×10-6(θ+33)-3.69×10-6θ4+2.33×10-5θ3+1.35×10-3θ2+5.42×10-2θ+5.588 θ=27°C when…

Q: Find the rate of change of 1/x with respect to x when x=2

A: f(x)=1xrate of change of 1/x with respect to x isdf(x)dxdf(x)dx=-1x2

Q: A 13 foot ladder leaning against a wall is pulled away from the wall at a constant rate of 3ft/s and…

A: Given,         A 13-foot ladder leaning against a wall is pulled away from the wall at a constant…

Q: Find the average rate of change on the given interval. Then find the instantaneous rate of change at…

A: Consider the provided equation, y=x+4x-1  from  x=2 to x=5 Find the average rate of change on the…

Q: What is the average rate of change of f (x) from x = 3 to x2 = 6? Please write your answer rounded…

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Q: Estimate the instantaneous rate of change at x=2

A: Please refer to the image below

Q: What is the average rate of change of the function f(x): = x² between x = -3 and x = 3?

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Q: Suppose a metal rod has length 20 cm and diameter 6 cm. If it is to be insulated, except for the…

A: Let the volume of the rod be V Radius of the rod be R and length be L Given: L=20cm; R=3 cm…

Q: Use differentials to estimate the value. estimate =  exact value =

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Q: at the point (2, –1). Find the maximum rate of change of f(x,y): x2 + Y

A: For maximum rate of change we need to calculate magnitude of gradient bat point (2,-1)

Q: What is the First Derivative Test for Local Extreme Values? Give examples of how it is applied.

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Q: A bacteria culture starts with 4 bacteria and grows at a rate proportional to its size. After 2…

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Q: An open cylinder can has an inside radius of 2cm and an inside height of 5cm. use the total…

A: We will estimate the volume of cylindrical metal as following. Inside radius = 2 cm Inside height =…

Q: Calculate the average rate of change of the given function over the given interval. Where…

A: Average rate of change of f(x) within the interval [a, b] is given by,A = f(b)-f(a)b-a

Q: A bicyclist is riding on a path modeled by the function f(x)=0.04(8x-x^2) , where x and f(x) are…

A: Given path functionfx=0.048x-x2

Q: i) What does it mean to say that the fixed effect varies cross sectionally by not over time?

A: Answer:----.                       Date:----28/09/2021

Q: Use the First Derivative Test to find the relative extrema of x – 3 f(x) ex

A: The given function is fx=x-3ex. We need to find the realtive extrema. Concept used:  Consider x=c is…

Q: What is the average rate of change of the height of the plant between Week 4 and Week 12, in inches…

A: Given:  Week Height (in inches) 4 24 6 27 8 30 12 48

Q: How to find the rate of change of y=x^2-3 over the interval (-2,0)

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Q: 7. How does the average rate of change for a square root function behave, for intervals of fixed…

A: Average rate of change can be found by calculating the change in y values of two points divided by…

Q: w many times between two points do we have an Instantaneous Rate Of change equalling Average ro

A: To determine the number of times the instantaneous rate of change equals to the average rate of…

Q: Find the average rate of change of g(x) = 7x* + on the interval [-1, 4]. %3D Question Help: OVideo

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Q: Find the average rate of change of the function between the given values of x. y = −5x − x2 between…

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Q: Find the average rate of change of h1x2 = x2 - 2x + 3:(a) From - 1 to 1(b) From 0 to 2(c) From 2 to…

A: Since it is known that the average rate of change can be calculated using the formula…

Q: Show that a constant function f(x) = b has an average rate of change of 0. Compute the average rate…

A: for a constant function f(x) = b average rate of change is zero because  function is same for all…

Q: The side of the base of a square prism is decreasing at a rate of 7 km/min and the height of the…

A: Surface area of a square prism is given by- A=2a2+4ah where a is side of prism, h is height of…

Q: 2. Use an example to show how to use the First Derivative Test for critical points

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Q: The volume of a cube decreases at a rate of 0.3 3ft/min. What is the rate of change of the side…

A: Let the length of each side of the cube be a ft. Find the volume of the cube. Differentiate the…

Q: Calculate first, second, and third derivative values for function, f(x) = -x2 + 5x + 3 at points x =…

A: Forward difference Consider a linear interpolation between the current data value (t0,I0) and the…

Q: A particle is moving along the curve y=4sqrt(2x+3). As the particle passes through the point (3,12),…

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Q: What is the rule for calculating the derivative of a composite of two differentiable functions? How…

A: Let us we consider a function which is real valued function which is composite of of two functions…

Q: It is known that a bacterial culture increases at a rate that is proportional to its current amount.…

A: Given- Number of bacterial fibers after 1 hour=1000 Number of bacterial fibers after 4 hour=3000

Q: Find the average rate of change of the function on the interval specified. h(x) = 5 − 6x2  on  [−2,…

A: To Find the average rate of change of the function on the interval specified. h(x) = 5 − 6x2  on…

Q: Compute the average rate of change of f from x, to x,. f(x) = 4x - 5, x, =4 and x, = 8 The average…

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Q: Obtain the relationship between marginal and joint characteristics functions.

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Q: Find teh average rate f change of f(x)=3x^(2)-x from x_(1)=-1 to x_(2)=2

A: Solution: The objective is to find the average rate of change of the given function

Q: What is the relationship between the secant line, slope of the tangent line, derivative of a…

A: Solved below

Q: ladder 5 meters long is leaning against a vertical wall. Due to the smooth floor, the foot of the…

A: Given query is to find the rate of change of y with respect to x.

Q: Compute the average rate of change of m(x)=x4  over the interval [a, a+x]. Simplify the expression…

A: Given:  m(x)=x4  To find average rate of change of the given function over the interval [a,a+x]

Q: A tank initially contains 200 liters of brine with 20 kg of salt solution. Brine containing 0.25 kg…

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Q: State the second-derivative test for functions of two variables.

A: State the second - derivative test for functions of two variable.

Q: What is the difference between a derivative and an integration?

A: We have to state the difference between a derivative and integral.

Q: Let g(x)=7arctan(5x). What is the instantaneous rate of change of g(x) when x=2?

A: g(x)=7arctan(5x) to find rate differentiate g(x) with respect to x

Q: A bicyclist is riding on a path modeled by the function  f(x) = 0.04(10x − x2),  where x and f(x)…

A: given: A bicyclist is riding on a path modeled by the function fx=0.0410x-x2 where x and f(x) are…

Q: What is the average rate of change of f between x=3 and x=10

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Q: 6. Use the difference quotient to estimate the 2 instantaneous rate of change in f(x) = x² at x=3…

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Exponential Growth Model

The relation that represents an exponential function is: