Consider the following function. f(x) = Find its average rate of change over the interval [1, 9]. Ду Ax Compare this rate with the instantaneous rates of change at the endpoints of the interval. f'(1) = f'(9) =

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: Estimate the instantaneous rate of change at x=2

A: Please refer to the image below

Q: 3.

A: Indefinite Integration

Q: The instantaneous velocity of a particle is defined as the derivative of some functions. Select one:…

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Q: Use forward, backward and central difference to estimate the first derivative of f (x) = In at x =…

A: Given function is fx=lnx and x=3 Step size h=0.01 We have to estimate the first derivative of fx=lnx…

Q: Suppose that the revenue (in dollars) from the sale of a product is given by R = 80x + 0.9x2 −…

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Q: 3. The derivative of /(x) = In x at x = 3 when hourrent = 0.001 and hprevious = 0.002

A: Given problem:- 3. The derivative of f(x) = In x at x = 3 when hcureent= 0.001 and hprevious = 0.002…

Q: Find the derivative of excosh(x)

A: Topic:- Derivative

Q: Estimate ln(0.9) using a linear approximation

A: Given:ln(0.9)

Q: Compute for the derivative of the function using logarithmic differentiation g(y) =…

A: Logarithmic differentiation: - The use of logarithms to derive the derivatives of some difficult…

Q: Find the second derivative and the points of inflection using the second derivative f(x) = ln(x) /…

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Q: Find the equilibria of the differential eq

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Q: The total derivative of f(x,y) = ylnx  is

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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: Determine the first derivative of the ff. function y = 2 + arctan(3 sec 2x)

A: We have to find the first derivative of the function: y=2+tan-13 sec 2x We know the formula of…

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: calculate the derivative

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Q: Estimate the instantaneous rate of change at the point x=2 for f(x)=ln(x) ROC =

A: the fiven function is f(x)=ln(x)

Q: Find the derivative of the function f(x) = ln(sinh x)

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Q: calculate the derivative with respect to x. ln x + ln y = x − y

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Q: Use forward, backward and central difference to estimate the first derivative of f(x) = In(x) at x =…

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Q: Find the derivative of the function

A: Given:y=arctanx+x1+x2Differentiate formula:ddxarc tanx=11+x2ddxuv=vdudx-udvdxv2

Q: Compute backward difference approximations for the first derivative of the function, y = log(x? +…

A: Given is the function y=log(x2+1)2   .  It is needed to compute backward difference approximation…

Q: Calculate the derivative of y=arctan√ex at x=0.

A: We differentiate both sides with respect to x using the chain rule.

Q: Find where the first derivative is equal to 0. Er ****. lif

A: Introduction: The concept of critical point is very important in Calculus as it is used widely in…

Q: Find the average rate of change of the function from x, to x,. Function x-Values f(x) = x² – 3x + 8…

A: The given function and x -values are: fx=x2-3x+8, x1=1, x2=5 Now, calculate the average rate of…

Q: a the derivative of h(x) = ln + 2 x5 et |

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Q: Find the derivative of the function y = arctan x+ 1+x?

A: To find: The derivative of the function . Calculation: Find the derivative of the function.

Q: Find the derivative of y given that y= x In x et

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Q: Find the derivative of the function y = cosh−1(3x)

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Q: Find the rate of change of f (x) = x° at x = 2. %3D

A: Rate of change.

Q: find the derivative of y with respect to x. y= ln3x

A: We can solve the given problem using chain rule derivative.

Q: what is the derivative of f(x)=ln(tanhx)

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Q: Suppose y=f(x) is a curve that always lies above the x-axis and never has a horizontal tangent,…

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Q: find the derivative of y with respect to x, t, or θ, as appropriate. y = ln3/x

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Q: Estimate approximate derivative of f(x) = x2 at x = 1, for h = 0.2, 0.2, 0.05, 0.01 using first…

A: Given function is fx=x2. We have to estimate approximate derivative of the given function at x=1 for…

Q: Use backward, forward, and centered difference approximation to estimate the second derivative of…

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Q: find the derivative of y with respect to the givenindependent variable. y = log25 ex - log5 √x

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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: Find the 2nd derivative of the given function fCt) = t² Int

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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: gives a good approximation, where t is time in years since 2007. Find the derivative function R'(t).…

A: The model representing the given data is defined by the function Rt=0.25t2-t+29 gallons, where…

Q: find the derivative of y with respect to the givenindependent variable. y = log5 ex

A: On simplification, we get

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

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

Q: Suppose x and y are functions of third variable t. In the equation *-+) , what are the values of the…

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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: 1 f(x) = (x² + 3x)² at [2,3]

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Q: Find the derivative of s(*) - L Int dt 1+t

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Exponential Growth Model

The relation that represents an exponential function is: