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

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: The tangent line to the graph of y=f(x)at the point (1,11) has the equation y=3x+8 (a) Find f′(1)…

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Q: Solve the first derivative of f(x) = e-2x In x at x 0.5 using forward finite-divided difference and…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

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 f(x) = a4 is the parent cubic function, prove that the AVERAGE rate of change of f(x) over the…

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Q: 2. Compute the second derivative, f"(x), of the function f(x) = e*. %3D

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Q: Find the derivative of the function 3 f(x) = V (x² – 2)' at x = -1. f'(- 1) =

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Q: Solve the first derivative of f(x) = 52x+1 at x = 0.5 using backward finite-divided difference and a…

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Q: Given the function f(x) = (x-2)2 + (y-3)2 (i) Find the critical points. (ii) Using the second…

A: The given function is: f(x,y)=(x-2)2+(y-3)2

Q: Compute the high-accuracy central difference approximation for the first derivative of y = cos x at…

A: There are three types of approximations to the derivative of a function f(x) at a point a. They are…

Q: Estimate the true percent relative error for the first derivative of the function, y =[eln)P, at x =…

A: We can solve this using Central difference formula f'(x) = (f(x+h) -f(x-h))/(2h)   The value of…

Q: 6. Determine the derivative of the function with respect to x. y = x2 – V2x +1

A: Solve the given problem.

Q: 3. Estimate the derivative of the function, f(x) = cos x + tan1 x, at xi= 0.5 using Richardson's…

A: To find the derivative of the function fx at x=x0 by Richardson's extrapolation centered finite…

Q: 3. Find the equation of the normal line to the curve f(x) = 6e2* cos x at the point (0,6).

A: Given: fx=6e2xcosx; 0,6 We know that for finding equation of normal at given point, we need to find…

Q: Find the average rate of change of f from 0 toπ/2 . f(x)=sin( x/2)

A: Derivative of a function determines the change of one variable with respect to another variable.…

Q: Consider the derivative function h (x) = 5x³ + 3x² – 4x + 4. What is the general antiderivative of…

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Q: Find the derivative of the function. f(z) = V - VE f '(x) =

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Q: Find the average velocity of the function over the given interval. y= - 3x? - x, [5,6] – X,

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Q: What is the 4th derivative at x = 0 of the function f(z) = (2r + 1)* %3D

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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: given the function f(x) = (x+4)^2 + (y-2)^2 (i)find the critical points (ii)using the second…

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Q: 3. The derivative of f(x) = In x at x = 3 when h = 0.002

A: 3) To find the true error and relative error of the function: f(x)=ln x, x=3 & h=0.002

Q: Find the weak derivative of f() = |x² – x + 1/5| on the 1) interval (0,1).

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Q: Determine the instantaneous rate of change of the function f(x) = [x² si sin (2¹) 1+√t x3 At x=1 dt

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Q: Find the first derivative or f'(x) of the function below using the techniques of integration f (x) =…

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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: * find the dicredional derivative af the. f omc tion and in the direction of a= [o,3, 37 + find the…

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Q: The derivative f'(a) represents the instantaneous rate of change of y = f (x) with respect to x when…

A: Given that we need to check  behaviour of  the statement " The derivative f'(a) represents the…

Q: 2. Approximate the derivative of f(x) forward, backward, and central difference method and step size…

A: To obtain the derivative at the point x0,y0, the following methods can be used:- The forward…

Q: Find the derivative of the function f(x) = V (x² – 2)* at x = 1.

A: Given f(x)=(x2-2)23      ⇒f(x)=x2-2213⇒f(x)=x2-223

Q: 4. F(x) = (1-t) dt

A: To find the first derivative

Q: Use Richardson extrapolation to estimate the first derivative of Y = sin x at * = π/4 using step…

A: Given the function  y=sinx

Q: Find the derivative of the function. 4 f(x) x In(x) f'(x) %D

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Q: For a function f (x, y), (0, 0) and (1, 1) are two critical points. Also, fxx = 2x², fyy = y²2 and…

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Q: The total derivative of f(x,y )=3 x+ 3 y-41n y is

A: Given function is fx,y=3x3+3y2-4 ln y find the total derivative  dz=fxx,ydx+fyx,ydy

Q: Find the particular antiderivative of the derivative f'(x) = 3 -+x that satisfies the condition f…

A: Follow the procedure given below.

Q: 42. f(x) = sec² x, [

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Q: Use Richardson extrapolation to estimate the first derivative of y = cos x at x = π/ 4 using step…

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Q: The domain of the function shown here is [Select ] The derivative of f(x) DNE at x=-1 because […

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Q: Find the linear approximation of f(x)=lnx at x=1and use it to estimate ln⁡(1.3) L(x)=? ln 1.3≈?

A: First find the linear equation at x=1  then find the approximate values

Q: 3. F(x) = " In(x) (4t + et) dt. Find the derivative of F(x).

A: Given, F(x)=∫1ln(x)(4t+et)dt To find : Derivative of F(x) By using the second fundamental theorem of…

Q: 1. Find the average rate of change in y with respect to x over the interval [1, 7]. 2. Use the…

A: Given that: The function is f(x) = 4x -3 .

Q: Consider the function f(x) = x³ Q 2: Calculate its first derivative at point x = 3 numerically with…

A: We have given , f(x) = x3

Q: Find the derivative of the function 4/ f f(x) = V (x – 3) at x = 2. f'(2) =

A: fx=x2-354⇒fx=x2-354 Differentiating with respect to x, we get f'x=ddxx2-354=54x2-354-1·dx2-3dx…

Q: The total derivative of the function f(x, y) =3x'y- xy is

A: Find the total derivative

Q: 4. The derivative of the function f(x) = r +3) is

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Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. F(x,…

A: SOLUTION-

Q: 1 f(x) = (x² + 3x)² at [2,3]

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Q: Find the derivative of the function. (x-7)(x²+2x) +3 y = O A. OB. dy dx O D. dy dx dy O C. dx dy dx…

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