x³-2 is x*+81 The domain of the function f(x)%3D Select one: (-0,-3)U(-3,3)U (3, 0) (-00,-3)U(-3,0) (-00,00) x-0 or x= ±3

Q: f(x)=x-1; g(x)=2x2 Find 1. (f+g)(x) 2. (f-g)(x)

A: Given, f(x) = x - 1 g(x) = 2x2

Q: x-8 Let f(x) = 3x +8, g(x) = x²+ 7, h(x)= - 3 Find (g ohof)(8).

A: The given function,fx=3x+8, gx=x2+7, hx=x-83

Q: 5 - x 4 – x2 Determine where f (x) = is continuou - O (-0, -2) U (-2, 2) U (2, 5] O (-00, 5] O (-00,…

A: Given function is, f(x)=5-x34-x2

Q: f(x) — — Зх -2 А. Domain : (-0о, 00 Range : (-0, x) В. Domain : (-0, 0 Range • 21

A: here option A is true

Q: e3x Let F (x) = In tdt then F'(x) = 9xe3x - 3x°e+³ 6xe³x – 3x°e* - 3xe3x - 3x° e* 9xe3x - 3x e* ...

A: From lebnitz test.

Q: f(x) = 2x³ -2x² + 5x-7 %3D g(x) = 5x3 + 2x² + x+2 find f(x) - g(x) %3D

A:

Q: 8. f(x) =x' -2x -7x-4 A) -1 (multiplicity of 2), 4 C) -4, 1 (multiplicity of 2) B) -4, 2…

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

Q: x- 3, x 1' find f(3)

A: f(x)=x-3,   x<1x2+5,   x≥1   Now we have to find the value of f(3)   Here, x=3, which is >1…

Q: F(x)=6-2x, 1<x<5

A:

Q: 8 6. * f(x) = 7 + + find f'(x). - x2 Find f'(2). | 8

A: To find the derivative we use power rule of derivative formula. Power rule of derivative is…

Q: 2x-3 3. Let f(x) = 3x+4' ,find Y as Ax -0 Ay

A:

Q: Graph the functions in Exercises 25–28.

A: "Since you have posted a question with multiple sub-parts,we will solve the first three sub-parts…

Q: .2 x -4 x + 2 f(x)={ x-2 at the point x = : 2 5 x = 2 |1-x, x 1

A:

Q: f(1)= f (3) =. f(4) =. x1 f(-1)= f(1)= f(0) =. f(2 5)

A: Given: (4). f(x)=4-x2,x&lt;132x+32,1≤x≤3                 { x+3,         x&gt;3 (5). f(x)=1,…

Q: X x-6 (a) f(x + 1)) 7. f(x) = 8. [x²-3, x≤-1 x + 4, x>-1 g(x) = (a) g(-2)) (b) f(0) (b) g(3) (c)…

A:

Q: f(x)= -2x -1 g(x)= -1/2 (x-2)^3 -5 Determine where g(x)>f(x)

A: Given fx=−2x−1 and gx=−12x−23−5 We have to determine where gx≥fx Now, solve gx≥fx…

Q: f(x) Let h(x) = , where f(-3) = 7,f'(-3) = –9, g(-3) = -2, and g'(-3) = 1. What is h' (-3)? |3D…

A:

Q: f (x) = *-1 and g(x) = 2 7 x-3'

A:

Q: 3. f(x) = x+2 4. f(x) = /2 x-7/ when x -3.8 (x-3, x<1 5. f()-1+5, x21' table of val:

A:

Q: 32) f(x)=3– 2 34) g(x)=(x – 1)³ +2 - 1 36) f(x) = I+1 38) f(x)=- 4 - 2x +1 40) g(x)=- %3D 3

A: Given ,f(x)=3-2x5That is ,y==3-2x5A function g is the inverse of function f if for y=fx,  x=gy…

Q: Given the functions            g(x) =   5x - 2      find g-1(x)…

A: The given function is gx=5x-24x+3. Replace x by y and gx by x and then solve for y as follows.

Q: 9. f(x) = 2x + 2, h(x) = -2x – 5 find (g o h)(-4 + x) 10. f(x) = 2x, g(x) = -x – 4, find (f o g)(x)

A:

Q: The profit function of Acrosonic company is given by P(x)=-0.02x^2+300x-200,000 dollars, where x is…

A:

Q: x²-9 Q.1. Let f (x)={ x-3 . Find the value of k for which |inmf (x)= ƒ(-3) X->-3 k² -5k +6,x=-3

A: f(x)=x2-9x-3,x≠-3k2-5k+6,x=-3

Q: x+x-30 Given f (x) = %3D x- 5

A:

Q: x2-6 Which of the following describes the end behavior of g(x) = as x approaches negative infinity…

A:

Q: f(x + Ax) - f(x) f'(x) = lim %3D Ax Ax-0 Differentiate: f(x) = x² + 4x - 3 CHOICES: (Just type ONLY…

A: Using given first principle of derivatives

Q: f (x) = - x + 43x - 5 %3D as x → -00 f (x) →-0 as x -∞f(x) -8 | as x +oof(x) → -8∞ as x → +of (x) →…

A:

Q: e* -1 f(x) = graph on the interval [-2, 2].

A: As per the instruction, we will be answering only the first one. For (a), We are given the function…

Q: f(0) =0, f(1) = 38, f(2) =16, f(-2)=-16, f(-1)=-38 f'(-2) = f"(-1) = f'(1)= f'(2)=0 f'(x)> 0 for x…

A:

Q: %3D 5. Find (f g)(2) if f(x) = x+ 2 and g(x) = x2+4x +4. O (f-9)(x) = + 2 O (f 9)(a) = +2 O (f 9)…

A: Given function are f(x) =x+2 and g(x) = x2+4x+4, we have to find the value of (f·g)(x).

Q: F(x)=x+7 & g(x)=2x-3 what is (f-g)(x)

A: Givenf(x)=x+7 &amp; g(x)=2x-3

Q: 3. f(x)=; X+5 X-4 4. f(x)= |x-1| Find (a) f(-3) Find (a) f(-1) (b) f(-3) + 4 (b) f(-1) + 2 (c)…

A: Given functions:- 3. fx=x+5x-4 4. fx=x-1

Q: EXAMPLE 1 Find where the function f(x) = 3x* – 4x³ - 120x? + 1 is increasing and where it is…

A: Given: fx=3x4-4x3-120x2+1 Derivative given function with respect to 'x' . f'(x)=12x3-12x2-240x…

Q: ² -9, x 3 3. f(x) = {2-x, -2 2

A: 2. Given, The function f(x)=x2-9,    x&lt;33,            x=39-x2,     x&gt;3 Clearly function is…

Q: f(x) 9(2) where f(-3) = 7, f' (-3) = –9, 9(-3) = –2, and g'(-3) = 1. What is h' (-3)? Let h(x) Do…

A:

Q: 2x-3 5. Let f(x) = find as Ax - 0 Ax 3x+4'

A: Given that: f(x)=2x-33x+4

Q: x2,   x≥0       -x2,  x<0   Find f'(0)

A:

Q: Identify the point of diminishing returns for the input-output function. R is the revenue and x is…

A: Consider the given input-output function, Rx=-25x3-4x-4, on the interval 0≤x≤3. The point of…

Q: 9. f(x) = 2x-1 and g(x)= -3x Find f(-1) +8 %3D

A:

Q: x+3 Jika fungsi f(x) = ***, maka f-(x) = .. 2 A. 2x + 3 В. 2х — 3 x+3 С. 2 c. ** D. -x+3 2. E.

A: The given function is, fx=x+32y=x+32 To obtain the inverse first step is to interchange y and x.…

Q: f(x) = , f (x) = , "(x) = 2-0) X-2 %3D 4-X 2(x-6) f" (x) %3D x3 x4

A: I think by giving the 3 function you mean to find the increasing and decreasing nature of the…

Q: x2 + x - 7 f(x) = %3D x² - 7 f'(x) = %3D

A: We have f(x)=x2+x-7x2-7 By quotient rule, we get

Q: 1 and g(x)=x² +2, then go fmay be expressed as x-2 axa + 2ßx + ¥ χα + βχ - β If f(x)=- g(f(x)) = =…

A:

Q: - 1) = 3 If h(x) = xf(x)g(x) and f(- 1) = 2, f'(- 1) = - 3, then determine the value of h'(- 1).

A: According to our guidelines, In case of multiple questions we are supposed to answer the first…

Q: 6. f(x) = x² – 4x, g(x) = 2-3E %3D a) (f - g)(-5)

A: Given: f(x)=x2−4xg(x)=2−3x

Q: 2. -3 3. f(x)= ;x = -1

A: See the details solution in below

Q: х-3, x 2 if x= - 5 is Blank 1

A:

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.  

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.