Find a formula for the average rate of change of f (x) = x^3 over [2, x] and use it to estimate the instantaneous rate of change at x = 2.

Q: Estimate the instantaneous rate of change of the function f(x)=−x2+4x−4 at x=1 using the average…

A: Consider the given function f(x)=−x2+4x−4

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: Find the average rate of change of f(x) = x² - x + 1 from x, = 1 to x, = 3. %3!

A: We have to find the average rate of change of function fx=x2-x+1 from x1=1 to x2=3. We know average…

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: What is the average rate of change of the function f ( x ) = 3 x over the interval [ 2 , 5 ]

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Q: What is the average rate of change of the function f(t) = -3t between t--4 and f--3?

A: what is average rate of change of the function f(t)=t2 -3t between t=-4 and t=-3   answer  put t=-4…

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

A: The given function y and the values of x between which the average rate of change of y is to be…

Q: Estimate the instantaneous rate of change of P(x)=5/x+2 at the point x=2

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

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Q: (a) Find the average rate of change of f(x) from x = 1 to x = 2. 7 (b) Using the definition of the…

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Q: If the instantaneous rate of change of ƒ(x) with respect to x is positive when x = 1, is ƒ…

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Q: Find the average rate of change of f(x)=x² – 5x from: x, =-1 to x, = 3

A: We will find the average rate of change of the function.  We know,  the average rate of change =…

Q: Compute the derivative of y = ln ( – V1 – 2 cosh x (x° + 2) |

A: To compute the derivative of,  y=ln1-2 cosh x .x3+2x.x-1.

Q: Find the derivative of the function. F(x) = et dt

A: The function is given as F(x)=∫xx2et4 dt. The Leibnitz rule of differentiation under the integral…

Q: Find the average rate of change of the function over the interval [-2, 1] f(x) = 2.x³ – 5.x +3

A: To determine the average rate of change of the below function over the interval [-2,1]. fx=2x3−5x+3

Q: Find the average rate of change of f from 0 to π /6 . f(x)= tan x

A: Given :           f(x) = tan x   To find the average rate of change of f from 0 to π6.

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: If the instantaneous rate of change of ƒ1x2 with respect to x ispositive when x = 1, is ƒ increasing…

A: As instantaneous rate of change  of f(x) that is f'(x) is positive means the function f(x) is…

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

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Q: What formula will describe the average rate of change of f(x) = 3* over the interval [0, 3]? Don't…

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Q: Find the total derivative of V with respect to X

A: As the differentiation is with respect to x, x becomes the variable. y and z becomes constants

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: Find the instantaneous rate of change of g(x) = In(x + 3) at x =

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Q: 2. What is the average rate of change of the function f (x) = x² – 3x over the interval [1,1.01]?

A: use average rate of change formula .

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

A: Rate of change.

Q: The average rate of change of fx) = ax' Over the interval osxs1 IS a

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Q: What is the equation of the normal line of f(x) = ln(x² – 3) at the point x = 2 ? %3D

A: Given:fx=lnx2-3  at a point x=2

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

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Q: Find the derivative of the function y = x tanh−1 x + ln√(1 − x2)

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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 average rate of change of LaTeX: f\left(x\right)\:=3x^2+1 f ( x ) = 3 x 2 + 1 between…

A: Formula for average rate of change is f(b)-f(a)b-a.

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: compute the rate of Change of the functioN at x= a. flx)= -2X²-X,Q= -5 instantaneous

A: Given function: fx=-2x2-x

Q: Use Dnf (x) to approximate the derivative of f(x) = sin(x) at ;h = (0.01,0.2) 4

A: Given fx=sinx at π4, h=0.01,0.2

Q: What is the average rate of change of f(X)= X2-2 on the interval [-1,3]?

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Q: Find the derivative of g(x) = fecost dt.

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Q: What is an average rate of change of function f(x) over the interval [1, 6]?

A: Function is the unique relation where each x is mapped to unique y. It can be of many type,…

Q: What is the 2nd derivative of y=cosh(x+y)?

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Q: Let m(x) be the slope of the tangent line to the curve y = 2x³-6x² + 3x at the point (x, y). Find…

A: Given: y=2x3-6x2+3x

Q: Find the average rate of change of the function on the interval specified Y=1/x on [1,3]

A: We know that ,The average rate of change of function over an interval a,bis given by f(b)-f(a)b-a

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: Let f(x)= 2x^3+3x^2-12x on [1,3] What is the average rate of change in f on [1,3]?

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

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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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Q: Find the average rate of change of the function f(x) = x 5x - 1, over the interval [-1,3

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Exponential Growth Model

The relation that represents an exponential function is: