49. The cost (in dollars) of producing x units of a certar modity is C(x) = 5000 + 10x + 0.05x². (a) Find the average rate of change of C with respe when the production level is changed (i) from x = 100 to x = 105 (ii) from x = 100 to x = 101 (b) Find the instantaneous rate of change of C wit %3D %3D %3D x when x = 100. (This is called the marginal - %3D significance will be explained in Section 2.7.)

Q: 19/9 10/9 Find any critical numbers for the function f(x) =x' whether the critical numbers lead to…

A: We need to find critical points.

Q: 22 dt at x = 4. ind the linearization of f(x) = 7 - 4 +t

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Q: 1 What is the lineur is The slope of the line tangent to the graph y = cos x at the point x =…

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Q: 5. Show that the function f(x)= 3x-9 is not differentiable at x=3. Find the formula for f'(x).

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A:

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A: Note: Since you have posted a question with two subparts, we will solve the first part for you.…

Q: 3 (a) Determine exact locations of critical numbers of the function f(x) COs x + cos 2x

A: for finding critical point take f'(x)=0

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A:

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A: f(x)=x4 at x=1 So, L(x)=f'(1)(x-1)+f(1)

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Q: Need help

A: Given function:

Q: 7) Find the average rate of change of the function K(x) = cos (x--) from x = 0 to x = 6

A: First of all find values of function at end points then put in formula of average rate of change.

Q: 1) Find the average rates of change of f(x) =x^3-3x a) from x1=-2 to x2= -1 and b) from x1=0 to x2=1…

A: 1.The average rate of change of any function (say y) is given by the formula -y =…

Q: 2 3 Use the first derivative test to determine the local extrema, if any, for the function f(x) =…

A: Take the derivative of f (x)  and equate to zero for finding point of extrema.

Q: 12. Consider the function f (x) = sin (nx). On the interval [0,3]. At what value of x would the…

A: Topic = Derivative

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A: As per the company guidelines we can solve first three parts. I hope that the given solution will…

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A: for f'(x) see 2nd and 3rd step. for g'(x) see 4th and 5th step.

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Q: 开3 Estimate the area under the graph of f(x)= 3x 3. between x= 0 and x =1 using each finite…

A: Note: As per our company guidelines we are supposed to answer the first three sub-parts of the…

Q: 49. GU] Find the smallest positive critical point of F(x) = | cos(r3/2) dt and determine whether it…

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Q: Differentiate the following

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

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A:

Q: 1. Consider the function F(x) = x³(x – 2)². a) Find all x values where F'(x) = 0 or F'(x) does not…

A: Critical numbers.

Q: The average rate of change of Ax) = x +x -x-1 over the interval o<xs1 is -2 1 O -1 2

A:

Q: 5. Find the critical numbers, and the intervals of increase/decrease for y=ln(4-x) %3D

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Q: 11 Use the Linear Approximation to estimate Aƒ for f(x) = when a 7+x? 2 and Ax = (Use decimal…

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Q: 98x2.1for one year to y

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Q: 13.Find a sinusoidal function with a maximum value of 9 that occurs at x=4 , and a minimum value of…

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Q: 4. Find two values of c in [-4, 4] such that f(c) is equal to the average value of f (x) = 3 cos 2x…

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Q: In an effort to make the distribution of income more nearly equal, the government of a country…

A: Given: Lorenz curve for first year: y = 0.97x2.1 And for the next year: y = 0.35x2 + 0.65.

Q: 84. Let f(x) = x' +3x² - 24x + 1 and g(x) =x' + 6x² - 36x + 1 . For what value(s) of x do both f(x)…

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Q: Estimate In 1.08 using the linearization L(x) of f (x) = In(x) at a = 1. (Use decimal notation. Give…

A:

Q: x = -1 is a critical number for g(x) = xª +x³ +x - 1. But the second derivative test fails for x =…

A: Explanation of the answer is as follows

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Q: Suppose the average costs of a mining operation depend on the number of machines used, and average…

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Q: 23 +5 z 1 Enter the value of 2 and of the derivative at that point, in the form æ2f'(x2). (d)…

A: Given :   f(x) = x3+5,x&lt;17x-x3x≥1 To find :  (a) To find the critical points of f(x).…

Q: or rage rate of change of f(x)=2+3x on t ve of f(x)=/2x-3(3x² +2)is 3x2 +2 b) 2/2x- 3 x-16 -3 (x-3,…

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Q: Show mathematically that MRS is increasing for U=1-ex +e2y and is diminishing for U=lnX +LnY

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Q: (2) Assume that we have a Cobb-Douglas production function for a certain industry: Q = CL°K®, where…

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Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, but…

A: Using the product rule of natural logarithm, it can be written that ln(ab)=ln(a)+ln(b) . Using the…

Q: 2. Consider the function h(x)=8+(x+3)*x"3 . a. Find all critical numbers for the function h(x).

A:

Q: 4. Find and classify all six critical points of f(x, y) = 3x – a³ – 2y2 + y*. Write your answers in…

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Q: 2.3 From the smallest to the largest, the three critical values of f(x) = x x-7 are

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Q: Suppose that the average cost, in dollars, of producing a shipment of a certain product is 20,000…

A: Suppose that the average cost, in dollars, of producing a shipment of a certain product as  C(x) =…

Q: 1 If f(x,y) =- and (x, y) changes from (3, 4) to (3.2, 3.9), x²+y² compare the values of dz and Az.…

A: