1) Find the absolute extremum values of f(x) = x2 – 4x + 18 over the interval [1, 4]. [2 marks]

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

A: The extreme value of function at f(3)= 30

Q: What is the critical point of the function f (x) = cos x? 2. What is the maximum point of the…

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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: In the function:  f(x)=(12−3x)e^x  What are the critical numbers of the function?  When is the…

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

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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: For the function f(x) = -2x + 3x2 + 12x 1. Find all the critical points of the function f(x). 2.…

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Q: Find value a  such that f(x)={x^2+2x-1 if x not equal to 1…

A: given,f(x)=x2+2x-1  if  x≠1a                if x=1left hand limit at x=1limx→1- f(x)=limx→1-…

Q: 2/3 Determine where the absolute extrema of f(x) = 3x25 - 2x on the interval [-1, 1] occur. The…

A: To find the absolute extrema of f(x) check the values of f(x) at critical points and at the end of…

Q: 1. Consider finding the root of f(x) =x´ – 5 use secant method, ɛ = 0, and start with the a interval…

A: given , f(x) =x2 - 5  we have to find roots of f(x) in interval by using secant method

Q: 22. (a) Find the critical numbers of f(x) = x*(x – 1)°. (b) What does the Second Derivative Test…

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

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Q: 3. Iff has a local maximum at x – 1, then what can you say about f'(1)? What if you also know that f…

A: Given: The function fx has a local maximum at x=1. First derivative test: Let f be differentiable…

Q: Find the absolute maximum value of f(x) = x² – 2x + 12 over the interval [0, 4]

A: Use critical value and end points for absolute maxima and absolute minima.

Q: 5. Find the absolute maximum value on the interval [0,16] for f(x) = (x² – 16x)5 and state its…

A: Concept: If a function f(x) define on interval [a, b] then it's absolute maximum occure either at…

Q: 12. Consider the function f(x) = 2x3 - 9x2 + 12x – 3. %3D (a) Find the critical values of f, that…

A: f(x) = 2x3 - 9x2 + 12x - 3 f'(x) = 6x2 - 18x + 12    [As derivative of xn = nxn-1]

Q: 3. Use Rolle's Theorem to show that the function f (x) = x² sin(x) – x sin(x) has a critical point…

A: For y = f(x). Let f(x) is continuous at every point of the closed interval [a, b] and differentiable…

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: 2. Find the absolute maximum and minimum values of f(x)= x³ – 3x +1 over the interval [0, 3].

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Q: 7) Find the absolute maximum of the function f on (0,E) S(x)= 10xe

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Q: 1. Use the Intermediate Value Theorem to show that there is a root of the given equation in the…

A: see 2nd step

Q: Find the absolute minimum of the function f(x)= = 02 GW/N 0.3 4 O 1 0-2 01 2 2x x2 +4 on the…

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

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Q: . (a) Find the critical numbers of . f (x) = x 4 (x -1 )3(b) What does the Second Derivative Test…

A: (a) We say that x=c is a critical point of the function fx if fc exists and if either of the…

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: 5x f(x) = on the interval[-3,1]. %3| x²+36

A: Given,           fx=5xx2+36 on the interval -3,1

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: for the funciton f(x) = x^3 - 75x Its local maximum  is____, which occurs at _____> Its local…

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Q: Find the absolute maximum value of f(x) = x² – 2x + 12 over the interval (0, 4]|

A: The absolute vale in the interval [0,4] for f(x) will be either at critical points or at end points.

Q: Find the absolute maximum and absolute minimum values of the function f(x) = 2x – 15 In(7x) on the…

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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: 1) Find the absolute extremum values of f(x) = x² – 3x + 15 over the interval [1,3].

A: To find the extreme values of the given function f(x) = x2 - 3x + 15 over [1, 3]

Q: 1. Find all the critical numbers of the function (Justify Your Answer) (a) [5Vx – 2 f(x) = x > 2…

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Q: The absolute maximum and absolute minimum for the function f(x) = x² – 16x [0, 9] a on the interval…

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Q: The Second Derivative Test cannot be used to conclude that x = 2 is the location of a relative…

A: We need to check for which of the given functions, can't conclude about location of  a relative…

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

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Q: Find the absolute maximum value of f(x) = x² – 2x + 12 over the interval [0, 5]

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Q: Find the absolute maximum and minimum values of f(x) = (x² + x)i over the interval [-3, 4]. absolute…

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Q: 7. Find the c value(s) that satisfy Rolle's Theorem for the function f (x) = x* – 4x² on the…

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Q: Find the absolute maximum value of f(x) = x2 – 2x + 18 over the interval [0, 5]

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Q: (b) Show that f(x) = ln(x + 2) has a unique fixed point in [0, 2].

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Q: Find the critical points that belong to the interval, as well as the absolute minimum and maximum…

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Q: 1. f(x) = x2 + x – 1 for all values of x %3D

A: A detailed solution is given below

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.

Q: 1) Find the absolute extremum values of f(x) = x² – 4x + 8 over the interval [1, 4].

A: f(x) = x2 – 4x + 8

Logic and Proofs

Discrete mathematics deals with the separated values of data such as integers. It is widely used in the practical field of computer science and mathematics. By knowing discrete mathematics one can improve their reasoning and problem-solving capabilities. Discrete mathematics became popular after the boom of computers which operate in discrete steps and store data in discrete bits. It also useful in studying computer programming, algorithms, and cryptography.