Find the number(s) b such that the average value of f(x) = 6x² – 42x + 39 - on the interval [0, b] is equal to 5.

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: Consider the function f(x) = 2x10 + 7x° – 6x² – 9. Enter the antiderivative of f(x) -

A: To find The anti derivative of f(x).

Q: How can we minimize the error of an approximation in a linear approximation at the point (a. f (a))?…

A: Query- How can we minimise the error of an approximation in a linear approximation at the point…

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

A:

Q: Suppose we have a revenue function given by R(z) = 6z- az?, %3D = 10? where a is a constant. What…

A: Given Rx=6x3-αx2 To find the value of α when average value is $20 for x=10

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: Find the average rate of change of f(x) with respect to x on the interval. f(x)= x^2 -5x+1; [-3,0]

A: f(x)=x2-5x+1;-3,0 We need to find the average rate change of f(x)

Q: Using a local linear approximation of f(x) = v4 + x at a 0 to estimate the value of v4.3 gives

A:

Q: What is the %ER of the approximate derivative of f(x) = x2ex , using forward-difference %3D approach…

A:

Q: Find the linearization L(x) to the function f(x)= Vx+4 at x =4, then use the linearization to…

A: linearlization of f(x) at x=a is  L(x) = f(a) + (x-a)f'a)

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: Use the second derivative test to identify any critical point and determine what each critical point…

A: Critical point: The point where the function fx, y is defined and its gradient is a zero vector or…

Q: 3. If f(r, y) = x*y - 2x-4y, then the total derivative of f

A:

Q: Find the relative extrema using both the first and second derivative tests. f(r) = 2x³ – 9x² + 12x.…

A: Consider: fx=2x3-9x2+12x. Critical point is the point where the derivative of the function is either…

Q: Find the average of the function g (x) = 2 cos 2x on the interval [0, r] -T

A: The function f(x)=2 cos 2x on the interval 0,π

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: Approximate X f(x) = e*over the interval [- 4, – 2] using 2 subintervals.

A: In this problem, Simpson 1/3rd rule is used to find the approximate value of e^x over the interval…

Q: Find the relative extrema of f (x) = 7+ 144x – 9x? using both first %3D and second derivative tests.…

A:

Q: Find the average rate of change of the function over the given interval. y =V4x + 1; between x 2 and…

A: To find the average rate of change of function y=4x+1 between x=2 and x=12

Q: Let f:[-n, 7] –→ R, where f(x) = 2 sin (2x) – 1. TC Calculate the average rate of change of f…

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Q: What is the linear approximation of the function f (x) = e x at x = 1?

A:

Q: Use differentials to approximate V36.1. 3.

A: Consider y = root x.Let take x = 36 and delta x = 0.1.Find delta y as follows.

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

A:

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

A:

Q: How can we minimize the error of an approximation in a linear approximation at the point (a. ƒ (a))?…

A:

Q: Find the linear approximation to f(x) = at a = 4.

A:

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 linear approximation of f(x) = (5 + x)n at x = 0. Use the approximation to estimate the…

A: fx=5+xn at x=0. Differentiating with respect to x, we get f'x=n5+xn-1 Now, f0=5+0n=5n &…

Q: What is the average rate of change of y with respect to over the interval [-1, 2] for the function y…

A:

Q: Find the average vale ot f(x)=Dx²e-2x overthe interval [-1,1]

A:

Q: Find the linear approximation L(x) to y = f(x) near x = a for the function. f(x) L(x) =

A:

Q: Find the best linear approximation to f(x) = ex on the interval [-1,1]

A: We have to find the best linear approximation of f(x)=ex on the interval -1,1.

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: 42. f(x) = sec² x, [

A:

Q: Find the linear approximation of f(x) = Vx-1 approximate 2.02. near a = 2. Use the result to

A:

Q: Obtain the MSE of f(x) = ex.

A: MSE = Maclaurin Series Expansion f(x)=ex formula f(x)=∑k=0∞f(k)(0)k!xk

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

A:

Q: Find the average rate of change of the function f(x) = 2x- 4x 8, on the interval r E [-3,2]. |3D

A:

Q: (1) Where on the line r = ay does the function f(r, y) = (x – a)² + (y – 2)² attain its smallest…

A: We need to check on the line x=ay.....................(1) if there exist a minimum for the function…

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: The average revenue is defined as the function R(x) Ř(z) (x > 0) Prove that if a revenue function…

A: Let Rx denotes the revenue function. The average revenue function is defined by Rx=Rxx where x>0.…

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

A: Find the total derivative

Q: Calculate the error of approximation E, for: f(x) = v3x + when x = 8. Ax = dx = 0.1

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Q: 2. Find the linear approximation of f(x) vx at x 4. Then, find the approximate value of 4.4 using…

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Q: The average revenue is defined as the function R(x) R(z) = (x > 0) Prove that if a revenue function…

A: Given average revenue defined as function R¯x=Rxx   x>0 To prove if a revenue function Rx is…

Q: Confirm the approximations by using the linear approximation at x = 0

A: