Let g(x) = |" f(t) dt, where fis the function whose graph is shown. y f 4 20 (a) Evaluate g(0), g(4), g(8), g(12), and g(24). g(0) =| g(4) = g(8) = g(12) = g(24) = (b) On what interval is g increasing? (Enter your answer using interval notation.) (c) Where does g have a maximum value? X =

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A: We have to find the linearization L(x) of the function at a.  We have, f(x)=9x and a = 3

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A: The given function is, f(x)=mx2-3x+1x-1,x≠1f(x)=n,x=1. That is,…

Q: Let f (x) = x² – 4. a. Find f'(x) using the formal limit definition of derivative. -

A: The formula of formal limit definition of derivative is  : lim h →0  [{f(x+h) - f(x)} / h ]

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A: We use L' hospital rule to find the limit.

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A:

Q: 1. A critical number of f′(x) is an inflection point of f(x). True or False 2. If the radius of a…

A: 1.A critical number of f′(x) is an inflection point of f(x).Answer:- True 2.If the radius of a…

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A:

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A: f: [0, 1] →R Domain: [0, 1] The function is discontinuous at a single point of the domain.   Let's…

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A:

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Q: I. Is the function given by g(x)=x²-3x + 2 continuous over the interval (-4, 4)? Why or why not?

A: Function given is- g(x)=x2-3x+2 continuous over the interval (-4,4) . Wee need to determine whether…

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A: Given: fx=x13 To Find: The derivative of the given function using limit definition

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A:

Q: 3. The graph of the continuous function g, the derivative of the function f, is shown above. The…

A: Given problem is :

Q: Sketch the graph of a differentiable function y = ƒ(x) that has local maxima at (1, 1) and (3, 3);

A: given that a differentiable function y=f(x) and has s local maxima at (1,1) and (3,3) local maxima…

Q: Where is the function f(x) = if x 0 removable discontinuity? Is it a jump discontinuity?

A: A jump discontinuity occurs when right and left limit exists but are unequal .

Q: 3. Sketch the graph of a function that is continuous, but not differentiable at I= 1.

A:

Q: State why the function 2z2 - 3z + e-z is analytic everywhere.

A: See the answer below

Q: 1. If F(x) = - eta dt, find F(1) and F'(x).

A: If Fx=∫exe et2 dt, then to find F1 and F'x.

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A: To find : function gx resulting from normalizing the function fx=x3-x4 defined in the domain 0, 34

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A:

Q: 2. Shows that the function f(x)- x2-9 is continuous at x = 0, but has removable x-3 discontinuity at…

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A:

Q: The critical points of the function f(x) 36z2 - 2x occur at 2- 0, r +4.00 0, z +2.40 %3D I0, z -…

A: We have to find the critical points of the function f(x)=36x2-2x4.

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Q: A continuous function y = ƒ(x) is known to be negative at x = 0 and positive at x = 1. Why does the…

A: Given that f(0)<0 and f(1)>0  f(x) is a continuous function.

Q: What are the maximum and minimum values of the function y = | x | on the interval -1 ≤ x < 1?…

A: Use the graphical approach to determine the maximum and minimum values of the function y = | x | on…

Q: Consider the following function. -x + 6x 10 f(x) 3D (a) Find the critical numbers of f. (Enter your…

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

Q: 4. Show the function f(2)=21m(z) is differentiable or not differentiable at any points.

A:

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A: In this question we have to find which statement is correct according to the given question.

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A: 1 st we will make differential equation for amount of salt and then solve it to get amount of salt

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A:

Q: A continuous function, h(x) has a local maximum at (2, 3). What is h’(2)?

A: We have given that h(x)  is a continuous function and has a local maximum at point (2,3).

Q: Let f(x)=kx^-1+x^2 For what values of k, function f(x) has a relative minimum but not a relative…

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Q: Estimate√16.2 using the linearization L(x) of f (x) =√x at a = 16. Plot f and L on the same set of…

A: To Determine: Estimate√16.2 using the linearization L(x) of f (x) =√x at a = 16. Plot f and L on the…

Q: Let F(x) = | f() dt where f(t) is the function whose graph is shown. Where does F(r) have a minimum…

A: Topic:- application of derivatives

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A:

Q: Find all critical points for the function f(x) = (z² – 4) . %3D

A: To find the critical points of f(x), find the derivative of f(x) and equate it to zero.

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A: Given, f'x=21-x21+x2                         ...(1) and f''x=4xx2-31+x22

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A: It is an usual example which derivative not vanish anywhere

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A:

Q: #8

A: Given:The decrease in weight from 487 pounds to 130 pounds in 8 months.