1. Show that the function f(x) = x³ – 3x + 1 satisfies the hypotheses of the Mean Value Theorem on the closed interval [-2, 2], and find a number c between –2 and 2 so that f(2) – f(-2) 2 – (–2) f'(c) =

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

A: Given: fx=2x−1x2+3x2+1, and gx=x2+872−3x25 To check whether: f'x=4x2x2−1+2xx2+3−2xx2+12x2−1x2+3x2+1,…

Q: Determine all critical points for the function. f(x) = x3 - 12x + 1 O x = -2, x = 0, and x = 2 O x =…

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Q: Consider a function f with domain {x|x 0} and the following derivatives: f'(x) = x2 4x - a and f"…

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

A: Given

Q: 11. Use the Mean Value theorem to show that f(x) = 2x sinh (æ – 1) + 2" – x has a critical number…

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Q: If fx) is a continuous function on [4,7] and F(x) is an anti-derivative of f(x) such that F(4)=9 and…

A: Given f(x) is continuous on [4, 7] and F(x) is the anti-derivative of f(x)                 F (4) = 9…

Q: 3 Given the function: f(x) = (1+ x)³/2 . x - 1 Prove that it is increasing on (0, +00) analytically,…

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Q: Find all the critical points and local maximums and minimums of each function. f(x) = 5x+cos(2x+1)

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Q: 9. Find the value(s) of k that makes the function continuous over the given interval. fx) = {3x + 4,…

A: Solve the question number 9 as asked by the user

Q: 7. Find the absolute maximum and absolute minimum values of f(z) = 2x – 3r2/3 on the interval…

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Q: 3. Given f(x) = x³ + x² – x + 1, on the interval bsolute maximum and minimum values, and indicate…

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Q: 1 Q9: Let f(x) = cosx x + 3 then find all critical points. 2 -

A: A critical number C is a number in the domain of 'f' for which eitherf'c=0 or f'cdoes not exists.…

Q: 2. A college professor never finishes his lecture before the end of the hour and always finishes his…

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

Q: Consider a function f with domain (xx 0} and the following derivatives: f(x) = bx-1 and f (x) = bx…

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Q: If f(x) is a continuous function on [3,7] and F(x) is an anti-derivative of f(x) such that F(3)=7…

A: Given :f(x) is continuous function 3,7Fx is anti-derivative of fxF3=7 and F7=3To determine…

Q: The function f has a continuous second derivative, and it satisfes f(2) = 5, f'(2) = 0 and f"(2) =…

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Q: 8. Consider the function f(x)=/25-x² . a. Find the linearization L(x) of f(x) at x=3.

A: Given expression is , fx=25-x2 to find out the linearization L(x) of f(x) at x=3.

Q: The function f has a continuous second derivative, and it satisfies f(-6) = -1, f'(-6) = 0 and…

A: Maxima minima problem....

Q: 2. Find the extrema of the function g(x) = x3 using any of the methods given in the above…

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Q: 1 4. Find the maximum value of f (x) = In(x- Inx) on the interval-<x<e. e

A: Given problem:- Find the maximum value of ƒ (x) = ln(x−lnx) on the interval 1/e≤x≤e

Q: 1. Find the critical numbers of the following function. f(x) = x-v*(x – 2)

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

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

Q: find the critical point for the function f(x)=2 x3+3 x2 - 72x+ 14 %3D O None O 4,3 -1,2 O 3,-4

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Q: find the value of a so that the function f(x)=xeax has a critical point at x=6

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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: In the function:  f(x)= (3x^2)ln(x) , x&gt;0 What are the x-coordinates of all local minima and…

A: Given:f(x)= (3x^2)ln(x) , x&gt;0

Q: 3. The function f(x) = x^4 − 4x^3 + 8x has a critical point at x = 1.(a)  Find f"(x).   (b) Then use…

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Q: Consider a function f with domain {x|x + 0} and the following derivatives: 2 bx3 bx² – 1 bx? f' (x)…

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Q: 3. Let f (x) = x ² + 8x + 14. Find all the values interral C-G ,2) such that f (c) = 0 of ċ in the

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Q: (b) Use Taylor's Theorem to give the Error Term E, (x) = f (x) – T, (x), as a function of x and some…

A: T2(x)=2+14(x−4)−164(x−4)2 The error term is…

Q: 12 11. Find the critical points of f(x) 4x? ). Then use the Second Derivative Test to determine if…

A: Here, we need to find the critical points of f(x)=x127x3-4x2. Now, f'(x)=6x2x-10xx and…

Q: Find the dérivative of the function: f(x)=In(e^x-13x)

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Q: 1. Identify all the x-values of the candidates for where you might find an absolute maximum or…

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Q: 6. Determine f such that f"(x) = 12x – 1 and 1 is both a critical number and a y- intercept of f.

A: A differential equation is an equation in x,y and derivatives of y. A linear differential equation…

Q: The function ff has a continuous second derivative, and it satisfies f(1)=2f(1)=2, f′(1)=0f′(1)=0…

A: Given: f(1)=1, f'(1)=0, f'(1) = 2 A critical point of a function occurs when the first derivative…

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: 4 If the critical number of the function f(x) =x is x 0, then the function %D is decreasing on (0,0)

A: We can find the decreasing interval as below.

Q: Suppose the function f(x)=3x^4+ax^3+bx^2 has a critical point at x=2, for which f(2)= −80. Determine…

A: Suppose the function f(x)=3x4+ax3+bx2 has a critical point at x=2, for whichf(2)= −80. Determine a,…

Q: Let f(x) = (2 – x)° f(x) has one critical value at A = | 0

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Q: 8) State the critical points of the function k(x) = x2 In x2.

A: Given,          The function kx=x2lnx2

Q: 2. Evaluate f(x) = e3x + 2 at x = -1. Round to the nearest thousandth. %3D %3D f(-1) = ...

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Q: Find the critical number(s) of the .4 * (function f(x)=In(2x)/(3x )2 نقطة( In(2x) f (x) 3x e/2 and 0…

A: Calculus

Q: LET F(X)=1/X.USE CENTRAL- DIFFERENCE FORMULA FOR F '(X) OF ORDER O(H4 ) WITH STEP SIZE H = 0.1 TO…

A: Given that fx=1x Step size h=0.1 To find f'2: Central difference formula for f'x of order Oh4:…

Q: 1. Consider the function z = f(x, y). If fa(a, b) and fy(a, b) both exist, and they are equal, then…

A: 1. Given: z=fx,y and suppose that fxa,b and fya,b both exists and they are equal and it is…

Q: If f(x) > g(x) >0 for X in [1,0) and g(x) dx diverges to +0, then | F(x)dx also diverges to +. True…

A: It is TRUE, that 0&lt;g(x)≤f(x) for x in [1,∞)  and                               ∫1∞g(x)dx diverges…

Q: Q.4 A/ Prove the function continuous at x = -2, (x2 + 5 13-3x where %3D if x<-2 if x 2-2 f(x) = %3D

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Q: 7. Find all values of x on the graph of f(x)=(x-1)´(2x+1) at which the tangent line is horizontal.…

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Q: 2. Suppose that f(x) is a function continuous for every value of x whose first derivative is f'(x) =…

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

Q: 2. The function (x) = x² is differentiable at x = 1. Find the function & such that o(x) = o(1) +…

A: Introduction: A technique for determining a function's derivative is differentiation. Mathematicians…

Q: 2. Find the principal part with respect to x for x 0 of the infinitesimal f(x) = = Vx + Vx. (That…

A: We have to use expansion of the function after some manipulations.