1 Answer the following questions about the function whose derivative is f'(x) = x a. What are the critical points of f? b. On what open intervals is f increasing or decreasing? c. At what points, if any, does f assume local maximum and minimum values? ++2).

Q: 2. Compute the derivative of the following functions: 1-e-* (a) f(x) = V1 – sin³ x, (b) f(x) =

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Q: Find the critical points of the following function. 2x f(x) = - x² +4 2x What is the derivative of…

A: Given,fx = 2xx2 + 4Differentiating the function;f'x = 2x×-1x2 + 42×2x + 1x2 + 4×2f'x = -4x2x2 + 42 +…

Q: 3. Suppose the function f has second derivative f"(x) = x2(x – 3)(x+2)*(? – 1). = T- (a) How many…

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Q: 1. Use limits to find the derivative of the following function at the point a = -1. 1 2x + 1 f(x)= =…

A: We have to find derivative

Q: 6. Find the tangent line to the function f(x) = 2x cos"(x) (0, 1).

A: To find the slope we need…

Q: Find the value of the derivative (if it exists) at each indicated extremum.           f(x) = cos x/2

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Q: Answer the following questions about the function whose derivative is given below. a. What are the…

A: Given: f'(x)=3sinx-32cosx+1, 0≤x≤2π To find: a) Critical points of f. b) The intervals in which f is…

Q: Answer the following questions about the functions whose derivativesare given:a. What are the…

A: Given: And

Q: Use the graph of the first derivative function f'(x) to find x values at which function has relative…

A: First of all, consider the graph of f '(x).

Q: Consider the following function on the given interval. (x) = 17 + 2x - x?, [0, 5) Find the…

A: Given f(x)=17+2x-x2  and the interval [0, 5] differentiating with respect to x, f'(x)=2-2x

Q: 2. Let f(x) = x² ln x + 1. Use the second derivative formula to approximate f"(1) when h = 0.2. %3D

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Q: The second derivative for the following function at x = 2 f(x) = v2x + is O 1 O 1/4 O 1/2 O 3/4

A: Use the basis concept of integration and derivative than simplify.

Q: 2. Let f(x) = /1 – x² . Find f(8) (0), i.e., the eighth derivative of ƒ evaluated at the point 0.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Answer the following questions about the function whose derivative is f'(x)=(x-5)^2(x+7). a. What…

A: (a) For critical points:

Q: 6.) What is the derivative of f(x) = x| at x= 07 a.) r'(x) = 1 c.) f'(x) = 0 b.) f'(x) is undefined…

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Q: Suppose that the first derivative of f(x) = x² In x is approximated by the following formula f'(x) ≈…

A: Note: According to Company Guidelines we are providing the answer of first question. Kindly post…

Q: Answer the following questions about the function whose derivative is f'(x) = (x-8) (x + 9). a. What…

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Q: Q2:A/ Consider the function f(x) = 11x+3 -what are the first and second derivatives? -what are the…

A: We will answer the first three subparts of the first question as per our guideline. Please resubmit…

Q: 6. Find the first order derivative with respect to z of the function u = In/x2 + y2 +z²

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Q: (e) Use a backward finite difference approximation to approximate the first derivative of the…

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Q: 55. By normalizing the function f(x)==-defined in the domain [0, 2], we will get as a result the…

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Q: Question 1 Find a classify the critical points of f(x)=-, using the two methods we learned in class:…

A: The given function is :f(x)=x55-x33 To find: Critical points of f, and  we need to classify them…

Q: Answer the following questions about the functions whose derivativesare given:a. What are the…

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Q: Answer the following questions about the function whose derivative is f'(x)= (x+3) e 2x a. What are…

A: Let us consider a function f(x). A point x=a is said to be a critical point of f(x) iff f'(a)=0 f(x)…

Q: Answer the following questions about the function whose derivative is f′(x)=(x−2)^2 (x+7). a. What…

A: We have to find

Q: Answer the questions below about the function whose derivative is f'(x) = 3 - 108 ,X#0. a. What are…

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Q: Can you help me with this problem step by step?

A: Consider the given derivative function.

Q: Find the 3rd derivative of f(x) at x = 1.15 using the second order accuracy formula. Present your…

A: .02

Q: #4) Given the function f (x) =x³-x² +2x- 1. Use the second derivative test, where applicable, to…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 3 Consider the function f(x) = 2+ 1+ (x+1)? Compute the derivative f'(x) . Determine all of the…

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Q: 1. Consider the function f(x) = v2 – x. a) Use the limit definition of a derivative to calculate f…

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Q: -) Givea the following data table= 国间。间 28 f(x.)- X, 2 42 3 50 Use Second-order finite difference to…

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Q: Find a linearization at a suitably chosen integer near a at which the given function and its…

A: To find a linearization at a suitable chosen integral near a= 0.11 at which the below function and…

Q: Find a linearization at a suitably chosen integer near a at which the given function and its…

A: To determine the linearization for the function.

Q: Answer the following questions about the function whose derivative is f′(x)=x2(x-3)/x+6. Assume the…

A: To determine:Part a) The interval of increasing and decreasing f.Part b) The local maximum and…

Q: 15. Find the linearization of f(x) = vx +1 at a = 15 and use it to find an approxima- cion to v15…

A: Given: f(x)=x+1 at a=15

Q: (e) Use a backward finite difference approximation to approximate the first derivative of the…

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Q: Answer the following questions about the function whose derivative is given below. a. What are the…

A: f'x=6sinx-62cosx+1,  0≤x≤2π a. Critical points are the points at which first derivative is zero.…

Q: Show that the function f(z) does not admit an anti-derivative in the domain N = C\{0}. Does it admit…

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Q: find a linearization at a suitably chosen integer neara at which the given function and its…

A: The given function is fx=1+x. The derivative of the function is, f'x=1. At point a = 8.1,…

Q: Answer the following questions about the function whose derivative is f'(x) = (x - 6)“(x + 9). a.…

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Q: Consider the following function. h(x) = x−1⁄3 (x − 14)   A) Find the derivative of the function. h…

A: Since you have posted multiple questions we will solve only two for you. If you want any specific…

Q: 1 as follows: Let f(x) = 1 Use linear approximation, i.e. the tangent line, to approximate %3D 1.003…

A: fx=1x Differentiating with respect to x, we get f/x=-1x2 Let us find the linear approximation at…

Q: Define h(x) = x° sin(1/x) for x # 0 and h(0) = 0. Prove that h is differentiable at x = 0, and find…

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Q: Suppose f is a function such that f(z) = 4z' and f" (z) = 12z. Which of the following is TRUE? f has…

A: Suppose f is a function such that f'(x)=4x3  &  f"(x)=12x2

Q: Зх +1 a) y =- 1 b) g(x)= Jx -

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Q: find a linearization at a suitably chosen integer neara at which the given function and its…

A: Given: fx=xx+1 We want to find a linearization at a suitably chosen integer near a at which the…