1. Solve the following: |X - 4| |X- 2 (b) 2 (a) 2 3 < 1 (c) 3 4 (x 3) < 1

Q: Solve the following problem min f(x1, x2, x3) subject to x1x2x3 xi + x2 + x3 = 1 ||

A: Minimum value of the function by lagranges multipliers method

Q: If f(1) =1 and f (x) 2 3 for 1 <x < 3, how small can (3) possibly be?

A: We will find the smallest possible value of f(3) as following.

Q: find a general formula for f (n)(x). f (x) = x−3/2

A: Given, f (x) = x−3/2 To evaluate, fn(x)

Q: 53. Suppose that f(x) = 3 sın x. 3. (a) Solve f(x) 2. %D (b) For what values of x is f (x) > on the…

A: Find your answer below

Q: Find a general formula for f (n)(x). f (x) =x-2

A:

Q: 11 When 2x' + x² – 2kx + f is divided by x – 1, the remainder is -4, and when it is divided by x +…

A:

Q: P(4<X<5)

A: Given that X is a continuous random variable. The probability density function is given as, fx=x8…

Q: (ii) Find the set of values of k for which |(x- 4)(x+2)|=k has four solutions.

A: Let's find.

Q: 8. Given that |f'(x)| < 1/3 for all x, and f(4) = 0, what can you say about the value of f(10), and…

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Q: What is the value of f(1) - 16B in 1 x³ Inx dx = f(x) ( (1/4) Inx - B) + C? 0 2

A:

Q: 6. Suppose f(x)-<ɛ. Solve for|x-1 where f defined below. x 1 f(x) = 2 3

A:

Q: 24. Solve the problem. Зг. If f(x) : f (3) = 0, and f(-6) is undefined, what are the values of A and…

A:

Q: 2. If f (2) = 10 and f' (x) = x²f (x) for all x, find f"(2).

A:

Q: If f'(x) > 3 for all x and f(2) = 5, what can you conclude about f(4)? %3D

A:

Q: If f(1)  = 10 and  f'(x) ≥ 2   for 1≤  x ≤ 4, how small can f(4)possibly be?

A: Given that f(1)  = 10 and  f'(x) ≥ 2

Q: 12 If f(x)+g(x) and f(x)-g(x) are divided by (x+1) and the remainders are 2 and -5 respectively,…

A: The remainder theorem says that DividendD=Divisord×QuotientQ+RemainderR That is D=d×Q+R Now, when…

Q: If f(1) = 12 and f '(x) 2 2 for 1 < x < 5, how small can f(5) possibly be?

A:

Q: If f(3) = 11 and f '(x) ≥ 1 for 3 ≤ x ≤ 6, how small can f(6) possibly be?

A: Given,          f3=11 and f'x≥1 for 3≤x≤6.

Q: ? Suppose that * f(3) = 1, and f(x) > 0, and f(x) < 0. Is it possible that f(2) = 3 4

A: Given fι 3=12  and    fιx&gt;0and fιιx&lt;0 . it is possible that fι2=34let g3 =  fι 3=12    ,…

Q: If f (1) =10 and f ʹ(x) ≥ 2 for 1≤ x ≤ 4, how small can f (4) possibly be?

A:

Q: Given, F(x) = 2x+3/4x+5 for x ne-5/4; f^-1(x)

A:

Q: Determine the error term of for the formula: f'(x)  ≈ (1/4h) [f(x+3h) - f(x-h)]

A: In order to find the error term of the given expression, first find the value of f(x+3h) and f(x-h).

Q: 1. Suppose: f(x) = 2x + 5, g(x) = - x². a. Find g 8(S(x)) 'b. Is g(f(x)) one to one? Justify your…

A:

Q: 4. What is the value of d in f (x) = 2x3 – 7x + d such that x + 2 is a factor of f (x). a) 1 b) 2 c)…

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Q: 9) Solve for f '(x) given f(x)= 2*

A:

Q: Give the formula for f(n) (x) where f(x)= 1/(3x-1)

A:

Q: 1- x**! 1- x n+1 6 (x # 1) r=0

A:

Q: 6. If f(x) =-2x + ax? +2 and f(2) = 2a, find a.

A: The given function is fx=-2x3+ax2+2. It is given that f(2)=2a.

Q: If f(4) 8 and f '(x) 2 1 for 4 < x < 9, how small can f(9) possibly be?

A: Given:- If f(4) = 8 and f '(x) &gt; 1 for 4 ≤ x ≤ 9 To find:- How small can f(9) possibly be?

Q: 1. f (x) %3D Зx? + 2х 5 3 5 X- х- 2f (x) = 2 х+ 4

A: your input value missing sign . let us consider its positive sign between 2x+ and 5 Given…

Q: Show that x - c is not a factor of f (x)for anyreal number c.

A: We have given fx=-x4-3x2-2 We can see here fx&lt;0 for all x belong to set of real numbers. If x-c…

Q: 1 = 3 for x Solve x – 1

A: The answer follows as:

Q: a) Suppose that f(3) = 15, f'(3) – 5 and let H(x) = Vf(x)+ 10. Find H'(3). b) Let f(x) = cx +…

A: (a) Differentiate the function Hx with respect to x to find H'x.

Q: Discrete

A:

Q: If f(2) = 2 and f '(x) ≥ 3 for 2 ≤ x ≤ 6, how small can f(6) possibly be?

A: given that f(2)=2,f'(x)≥ 3 for  2 ≤ x ≤ 6. we need to find how small can f(6) can be We use Mean…

Q: 5 2 7 . If f(x) = 3 + 4x · 2* + r", what are f"(0) and f"(0)? 3!

A: Given f(x)=3+4x-52!x2+73!x3

Q: 26. f(x)=-3x +2x? – x+4 27. f(x)=x -8 28. f(x)=x -2x* – 3x° +x³ – x² +10x+2

A: As per our guidelines we are supposed to answer only first three parts.kindly repost others part as…

Q: x for – 1 5 10- -2 10

A:

Q: If f(1) = 6 and f'(x) > 2 for 1 <æ< 3, how small can f(3) possibly be?

A:

Q: If f(3) = 7 and f ′(x) ≥ 2 for 3 ≤ x ≤ 5, how small can f(5) possibly be? f(5) ≥

A:

Q: If f(3) = 2 and f '(x) 2 1 for 3 < x < 6, how small can f(6) possibly be?

A:

Q: If f(1) = 5 and f'(x) > 2 for 1< x < 6, then the smallest value of f(6) would be

A:

Q: 3 Suppose f (x) = If 5х — 4 [s(x) dx=A/5x- 4 +C, for constants A and C, what is the value of A?…

A: Given: f(x) = 35x-4 ⇒f(x) = 35x-4-12 ∫f(x)dx = A5x-4+C

Q: ind the values of k for which f(x) = kx3 -9kx2+9x+3 is increasing on R

A: Definition used -                  Interval of increase -                    A function f(x)…

Q: Suppose that the cost for manufacturing n desks is C dollars, so we have C=f(n). Which of the…

A:

Q: If f(3) = 14 and f '(x) ≥ 2 for 3 ≤ x ≤ 5, how small can f(5) possibly be?

A: The given conditions are,

Q: where P is the number of residents, and t is years after 1980 Compute P(0) and interpret its meaning…

A: Given that, P(t)=225t+7000,Where P is the number of residents and t is years.

Q: If (2)-3.f(2)-1, g(x)=1/x, and htx)-[fx)][g(x)], then what is h'(2)?

A: Given that h(x)=[f(x)][g(x)] So, using the product rule,  h'(x)= [f'(x)][g(x)] + [f(x)][g'(x)] Then…

Q: If f (2) — (г — 3)*, what is f' (2)? O f' (x) = (x – 3)°z o f (г) — 3(г — з)? O f'(x) = (x – 3)² O…

A: To Determine:  what is f'(x) that is find the derivative . Given: we have f(x)=x-33 Explanation: so…

Q: If f(2) = 7 and f '(x) ≥ 1 for 2 ≤ x ≤ 6, how small can f(6) possibly be?

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.