a.) What is the average cost C(x) per vest if x vests are produced in one​ day?   b.) Find the critical numbers of C(x)​, the intervals on which the average cost per vest is​ decreasing, the intervals on which the average cost per vest is​ increasing, and the local extrema.

Q: Assume that it costs that same company approximately C ( x ) =62,229+5,573x +0.033x 2 dollars to…

A: The given cost function is Cx=62,229+5,573x+0.033x2. It is known that, the average cost function can…

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A: Given Data: A producer of pedal-powered ice cream makers has determined that the revenue from the…

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A:

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A: Given: f(x) = ln(tanh(2x))…

Q: Consider the function f(x) = ax + b, where a and b are constants. Which of the following is one of…

A:

Q: 16. If f(x) = 2x² + 3x + 5, f(c) = 20, and the interval is [0,5], use the Intermediate Value Theorem…

A: If fx=2x2+3x+5,  f(c)=20,  [ 0,5]  f0=202+30+5 = 5  f5=252+35+5 = 70  Using Intermediate value…

Q: Find the largest open interval, centered at the origin on thex-axis, such that for each x in the…

A: f(x) = x +2 f(0) = 2 ∈ = 0.2   Now, | f(x)  -  f(0) | <  ∈

Q: Find conditions on a and b that ensure f (x) = x3 + ax + b is increasing on (−∞,∞).

A: Consider the given function as fx=x3+ax+b

Q: Is the function a. EVEN h ODD f(x) 1, -π<x<0 1, 0≤x<T

A:

Q: If f'(x) = x - 2x-x +2, thenf has a relative minimum at x= -2 O0 0 O0

A:

Q: Find the maxcimum profit and the number of units that must be produced and sold in or der to achieve…

A: Given that, Revenue function: R(x) = x2 + 110 x + 60 Cost function: C(x) = 1.1 x2 + 10 x + 80 We…

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A:

Q: Use Taylor's Inequality to estimate the accuracy of the approximation f(x) ≈ T₁(x) when x lies in…

A:

Q: Assume that it costs that same company approximately C(x) =62,229+5,573 x+0.033x2 dollars to…

A: Given, C(x)=62,229+5,573x+0.033x2 where x be the improved deluxe gameplay stations in an hour and…

Q: Given f(x) = In(x² + 3x + 9), over the interval [ – 5, - 1], answer the following: %3D a) The point…

A: Given,           fx=lnx2+3x+9

Q: The manager of a 100-unit apartment complex knows from experience that at a rent of $1500 per month,…

A:

Q: The marginal revenue (in thousands of dollars) from the sale of x gadgets is given by the following…

A:

Q: The value of k that makes x2 – kx + 2x – 2k f(x) x # -2 x + 2 4, continuous at x = -2 is x = -2 O 2…

A:

Q: Find the critical points of the following function. f(x) = 5x? + 3x +2

A: Given,          The function is fx=5x2+3x+2.

Q: At what interval is y=3x5-5x3 decreasing O x>1 O -1<x<0 O -1<x< OU 0<x<I O -1<1<l

A: We have to find interval where it is decreasing

Q: 7) Find the absolute maximum of the function f on (0,E) S(x)= 10xe

A:

Q: 1. Use the Intermediate Value Theorem to show that there is a root of the given equation in the…

A: see 2nd step

Q: Find the x-value corresponding to the absolute minimum value of f on the given interval. (If an…

A:

Q: 3 B Consider the following function, z= x -2xyty't yn Lind the alues of ag Ddz,z,when redgyel dy 6.

A: Given : z = x2 -2xy + y3 + yw

Q: Calculate the  M6  approximation for  f(x) = 4(x + 18)  on  [5, 8].   M6 =

A:

Q: (b) Suppose that f(x) = βx2 − 3          if x ≤ 2                                     βx + 2…

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

Q: 1. Apply the Parseval's identity to the function f (x) = x, –n < x < n

A:

Q: show steps please.

A: We will find the first two derivatives of F(x) We use the fundamental theorem of calculus To find…

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A:

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A: Here we have to calculate the time taken by the vehicle to reach the speed of 50m/s…

Q: Given f(x) = In(x² + 5x + 8), over the interval [ – 6, – 2], answer the following: %3D a) The point…

A: Given,          fx=lnx2+5x+8 over the interval -6,-2

Q: Suppose f is known to be differentiable and contains a local extremum at c, then which of the…

A:

Q: Suppose that the manufacturer of a gas clothes dryer has found that when the unit price is p…

A:

Q: The cost C of building a house is related to the number k of carpenters used and the number x of…

A: The solution for the above question is as shoewn below.

Q: A juice company has found that the marginal cost of producing x pints of fresh-squeezed orange juice…

A: Given marginal cost function, C'x=0.000008x2-0.004x+5, for x≤350 Find the total cost.

Q: The marginal revenue (in thousands of dollars) from the sale of x handheld gaming devices is given…

A:

Q: Let f(x) = ax* + bx . If (1,6) is a relative extremum point, then b is?

A:

Q: Calculate M6 for f(x) = 5 · In(æ³) over [1, 2].

A: Given:   f(x)=5.ln(x3) over [1,3]

Q: The absolute maximum of y =-x + 2x +3 on the interval [0, 3] occurs at Select one: O a. None of…

A: Simply take the derivative and equate to zero than solve for x.

Q: Suppose f(x) is continuous everywhere, and has the following values: 10 20 30 40 f(x) 9. 13 2 3 What…

A:

Q: Which values of C makes r(x) (a) left-continuous, (b) right-continuous (c) continuous x2 +3 for x 2

A: If the function r(x) is left-continuous, then use limx→-1-rx=limx→-1+rx, to determine the value of…

Q: Suppose h(x) = [,f(t)dt on the interval [0, 12], where f (t) is shown in the graph below. f (t) -4-…

A:

Q: Find the point of diminishing returns for the revenue function R(x)=-2/3(x^3-12x^2-6), 0 less than…

A: The given  revenue function is Rx=-23x3-12x2-6. in the interval 0≤x≤8. Since a point of diminishing…

Q: Find f(x) if f(3) = 0 and the tangent line at (x, f(x)) has slope x2 + 5 In (14) f(x) =| 히n 글미(구+ 5)…

A:

Q: Use the Intermediate Value Theorem to show there is a root of the given equation in the specified…

A: Intermediate value theorem states that if “f” be a continuous function over a closed interval [a, b]…

Q: If f(x) = then f (x) at z = 1 is

A: Given that :-         f(x)=1x         f'(x)=? at x=1

Q: A juice company has found that the marginal cost of producing x pints of fresh-squeezed orange juice…

A:

Q: For what values of h and k is h+2x , 15 x52 -2 < x<-1 2< * 2 - Continuous at every x ? 2x2 - 2x-4,…

A:

Q: 1) Find the absolute extremum values of f(x) = x² – 4x + 8 over the interval [1, 4].

A: f(x) = x2 – 4x + 8

Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.