1. If x is an exact measurement of a certain quantity and x0 is its approximation, the concept of error in the approximation is defined by [(a) X, - X (b) x-x |(c) x-X,

Q: 1) Find the absolute extremum values of f(x) = x² – 3x + 20 over the interval [1, 3]. [2 - marks]

A: We have to find the absolute extremum values of the given function.

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: (₁ Find the absolute extrema of the function on the closed interval. ƒ(x) = x³ − 12x + 1, [-3,1]

A: An absolute extrema of a function in a given interval is the point at which a maximum or minimum…

Q: Minimize f(x) = x² + 54 ; using Interval halving method for 2 ≤ x ≤ 6. E= 10-³

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Q: The function f(x) = 2x 36x + 210x – 4 has two critical numbers. The smaller one is x = and the…

A: Thw critical points are given below

Q: Find the length of the curve e^x / 2 + e^-x /2 between x=0 and x=1

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Q: 1) Find the absolute extremum values of f(x) = x² – 4x + 16 over the interval [1, 4].

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Q: The Standard Error of the Estimate will equal zero when___________________.     y = 0, and x = 0…

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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: Suppose ff is differentiable on (-\infty,\infty)(−∞,∞), f(3)=12f(3)=12, and f'(3)=-2f′(3)=−2. Use…

A: Given that,  Function f is differentiable on (−∞,∞), f(3)=12, and f'(3)=-2. The linearization of f…

Q: In(x) Find the maximum and minimum values of the function f(x) on the interval [1,6] by comparing…

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Q: 17. The function f(x) = x³ + bx² + c has a critical point at (-2, 6). Determine the value of b and…

A: Please follow the next step.

Q: 18. Solve for A and B so that f(x) has a limit at both x = 2 and x = 4. 3x + 4, x> 4 f(x) Ах + B,…

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Q: (b) A right-angled triangle has sides of length 3 and æ, and a hypotenuse of length e. Given that (2…

A: Given a right angle triangle has sides of length 3 and x and a Hypotenuse of length l. Given that…

Q: 1 8 (b) Determine the exact locations of the critical number of the function r(x) 3 х — 4

A: As per our guidelines we are supposed to answer only one question.* *Kindly repost other question as…

Q: 1) Find the absolute extremum values of f(x) = x² – 3x + 12 over the interval [1, 3].

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Q: 5. [ 4 ifx2 Show that f(x) = is not differentiable at x = 2.

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

Q: Please show steps.

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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: find the critical point for the function f(x)=2 x³ +3 x2 – 12x+4 X' 3,-4 O -1,2 O 1,-2 O None

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Q: - y = In(x – 2)

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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: 6. Locate the absolute extrema of the function H(x) = - x* Inx on 1 3 2' 2 Give exact solutions.

A: We have to find out absolute extrema

Q: Determine all critical points for the function. f(x) = x3 - 12x + 3 x = -2 and x = 2 Ox = -2 O x = 2…

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Q: The function f(x) = 2x° 39x + 240x – 11 has two critical numbers. The smaller one is x = and the…

A: Topic = Derivative

Q: 1. Find all critical points for the functions: a) f(x) = x² – 10x – 9 5 – x b) f(x) = x² – 6x + 30 -

A: As per our company guidelines we are supposed to answer only first question. Kindly repost other…

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: 1 5. By using the cubic approximation of f(x) = --1 around a = 0 in question 4, estimate the error…

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Q: 1) Find the absolute extremum values of f(x) = x² – 3x + 12 over the interval [1,3]. [2 marks] %3D -

A: Given: fx=x2-3x+12 over the interval 1,3

Q: 19. Solve for A and B so that g(x) has a limit at both x = -1 and x = 3. 4x - 2, X> 3 g(x) Ax + Bx +…

A: To solve for A and B so that gx has a limit at both x=-1 and x=3. gx=4x-2,       x≥3Ax2+Bx+2,…

Q: the critical points of f (x) are x = -2 and x = 1, and f '(0) = -6 we can conclude that in the…

A: Solve the following

Q: Use the linear approximation (1 + x)k = 1 + kx to find anapproximation for the function ƒ(x) for…

A: It is known by linear approximation that 1+xk=1+kx for the values of x near 0. The given function is…

Q: What is the critical point of the function g (x) = (x ^ 2/2) + x (ln (x) −1), using Newton-Raphson,…

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Q: 22) The critical points of the function F(x,y) = x³ + 3xy + y3

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Q: 1) Find the absolute extremum values of f(x) = x² – 3x + 10 over the interval [1, 3].

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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

Q: In Problem (A), Show that f(x, y) is differentiable at the indicated point. A) f (x, y) = (x2 +…

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

A: We use the quotient rule, product rule, and chain rule of differentiation to check the claim of the…

Q: 12. If a firm's profit function is T = f(Q) and the level of output, Q, varies between a and b…

A: Consider the given function. TR=1001-e-0.1Q and TC=0.1Q2+2Q+1 The profit function is defined as,…

Q: Find the absolute maximum and minimum values of f(x) = e * – 3x on [0,5].

A: f(x)=ex-3x Take derivative wrt to x f'(x)= ex-3

Q: Suppose that we don't have a formula for g(x) but we know that g(1) = -4 and g'(x) = V x2 + 15 for…

A: g(1)=-4, g'(x)=x2+15 Finding the value of g '(1) g '(1)=12+15=1+15=16=4

Q: The function f(x) = 2x – 33x + 60x – 8 has two critical numbers. The smaller one is x = and the…

A: To find the critical point use the differentiation .

Q: a) f(x)= x° (x – 4 )²

A: To find critical number of f(x)=x45(x-4)2

Q: The function if x 1 has critical points at... (Choose all that apply.) x = 0 x = -1 x = 3

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

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Q: If a company's marginal revenue function is  MR(x) = xe−x/9,  find the revenue function. [Hint:…

A: Consider the given marginal function.

Q: 3. Consider the function f(x) = r - 1+x 1- a. Explain why, when evaluated in a floating point…

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Q: Find the critical numbers of the functions below: f(x) = x^4/5 (x − 4)^2

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