Function g can be thought of as a translated (shifted) version of f(x) = |c|. %3D 7- 6+ 5- 3 -7-6 -5 -4 -3 -2 1 2 3 4 5 6 7 -2- -3+ -4+ -5+ -6+ What is the equation for g(x) ? Choose 1 answer: 8+1미= (x)6 g(x) = |x+ 3|

Q: The domain of the function f(x) = v2x- 3 is -) a) b) c) (-0,2] d) (-0,3] b d. a O c

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Q: ALUATE THE FUNCTION, if g(x² - 3); evaluate g(x) = 3-x/3+x

A: We have g(x)=3-x3+x to evaluate gx2-3

Q: The bar graph shows the percentage of people 25 years of age and older who were college graduates in…

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Q: True or false? Explain. If g (x)=x, then g-'x)-x.

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Q: Зх-2 p) Find the domain of the function f(x) 3D 5x2+4x-1

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Q: Find the slope of the graph of the function at the given point. f(x) = 2x4 − 4x3 + 6x2 − 14x; (1,…

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Q: Find the domain for the function. X-3 V3x-2 a) (-0, 00) b) (- ∞, 3) U (3, 0)

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Q: Find the domain of the function. f(x) = Vx-8 6. 8. f(x) = x2 + 8

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Q: Find the maximum or minimum value of the function. g(x) = 2x(x - 4) + 7

A: The given function is:  g(x) = 2x(x - 4)+7 This can be written as: g(x) = 2x2-8x+7 To find the…

Q: Differentiate the function. g(x) = 6x + 5

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Q: Find the domain of the function : g(x) = √(x-3) + √(x+4)

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Q: Differentiate the function. g(x) = (3+2x)/(7-8x)

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Q: The zeros of a function fx) are 3 and 4, while the zeros of a second function g(x) are 3 and 5. What…

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Q: Find the domain of the function : g(x) =2/(x2 + x - 12)

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Q: 9. What is the domain of the function f(x) = Vx- 3? | A. (3, 0) B. (-00, 3] С. [3, о) D. (-00, 3)

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Q: Find the relative extreme values of the function f(r) =-- 6r + 5. %3D

A: f(x)=x33-x22-6x+5f'(x)=x2-x-6x2-x-6=0x=3,-2For -∞,-2, f'(-3)=6>0For -2,3, f'(1)=1-1-6<0For…

Q: f(x)=-5x g(x)=8x^2-5x-9 find (f*g)(x)

A: f(x)= -5x  g(x)= 8x2  - 5x -9

Q: Given                         f''(x)=3x-2 and f'(-1)=-3.  and f(-1)=-3 find f'(x)=??????? find…

A: Integrate and satisfied given conditions

Q: Find the domain and range of the function. g(x) = x2 − 5

A: Given: gx=x2-5 we know that for any quadratic function whose coefficient of x2 is positive domain is…

Q: What is the end behavior for this function? F(x)=x^5-3x^3+2x-4

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Q: Find the range of the function f(x) = 1/3x-5, if the domain is { -3, 0, 6}

A: f(x)=13x-5Domain is -3,0,6substitute x=-3f(-3)=13(-3)-5=1-9-5=-114

Q: Example: find the extreme values of the function f(x, y) = xy – x² - y² – 2x – 2y + 4

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Q: f(x) = 2x + 7 and g(x) = x³ + x + 13 what type of function is (f + g)(x) ?

A: Given: f(x) = 2x + 7 and g(x) = x³ + x + 13 Our task: (f + g)(x) ?

Q: Calculate the value of f(-3) for the function f(x) = 3x^2

A: In order to find the value of a function f(x) at a point x=a, we just replace a at the place of x…

Q: Find the domain of the function.

A: The given function f(x) is - f(x) = x2+2x-13x2-4x-8For the function f(x) to be defined, the…

Q: x6 (x) 12

A: Given:  Given that a piecewise function fx=x,  x<-2x2-4, -2≤x<412,  4<x<68,  x=6-x+10,…

Q: P(x) = –x2 + 90x – 300 is a profit function where x is the number of items sold, and P(x) is the…

A: Given that, P(x) = –x^2 + 90x – 300 is a profit function where x is the number of items sold, and…

Q: Let h(x) = f(x) + g(x). If f(x) = 2x² and g(x) = 8x5, what is h'(x)? Do not include "h' (x) =" in…

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Q: Example: find the extreme values of the function f(x, y) = xy – x² -y² – 2x – 2y + 4

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Q: -3 -2 -1 у 1 - 1 -2 -3 -4 -5- 1 2

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Q: f(x) = x* + x³ – 2x² What is the domain of the function given above?

A: We have to find the domain of the given function

Q: x - 7 If f(x) = Vx – 3 and g(x) find the domain x - 4 of

A: Given: f(x)=x-3 and g(x)=x-7x-4 To find: Domain of fgx.

Q: What is (f + g)(x)? f(x) = -2x g(x) = x² - 7x + 6

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Q: -k/complete-a-table-and-graph-a-linear-function f(x) = 4x + 2 f(x)

A: f(x)=4x+2 at x=0 f(0)=4x0+2=0+2=2 f(1)=4x1+2=4+2=6 f(2)=4x2+2=8+2=10

Q: f(x) = -3x² + 2, g(x) = x + 2 Find f(-5) - g(-5).

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Q: 9 The slope of the function ƒ (x) = 8 - 2x is _____. -8 -2 2 8

A: here we have to find the slope of function  so we have to find dy/dx so differentiate the function

Q: Let h(x)=f(x)+g(x). If f(x)=x4 and g(x)=6x3, what is h′(−3)?Do not include "h′(−3)=" in your answer.…

A: The problem concerns addition law for derivatives of functions:

Q: The zeros of a functions Ax) are 3 and 4, while the zeros of a second function g(x) are 3 and 5.…

A: Solution

Q: What is g(f(-1))? -1 2 1 2 4 8. 16 g(x) -5 -3 -1 1 3

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Q: Find the domain of the function : g(x) = √(x-3) / x-6

A: Given: gx=x-3x-6 To determine: Domain of the given function.

Q: Find the domain of the function  F(X)= X^2+3

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Q: Consider function m. -8 -6 -4 fo m(x) 8- 6- 4- 2- -2- -8- What is the domain of function m? 8 X

A: Here given graph as

Q: f(x) = -5-8 g(x) = -3x² - 6x - 2 Find: f(x) g(x)

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Q: The linear function f with values f(-3) = 10 and f(4) = 7 is f(x) =

A: We can find the linear function as below.

Q: 3 4. Find the domain and range for the function f(x): 1- c2r

A: Given: The function fx=31-e2x, To find: The domain and range of the given function.

Q: Let h(x)=f(x)−g(x). If f(x)=9x2 and g(x)=8x, what is h′(−5)?Do not include "h′(−5)=" in your answer.…

A: We have been given two functions f(x) = 9x^2 and g(x) = 8x and a relationship between functions h(x)…

Q: c-x- 12 Consider the function f(x) %3D x+4

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: f(x) = x 2+ 4x g(x) = 2x + 5 Find f(-7) - g(-7)

A: Given: fx=x2+4xgx=2x+5 To find f(-7)  plug -7 in the given function f we get,…

Q: f(x)=x^2-3x+9 g(x)=3x^3+2x^2-4x-9 find the (f-g)(x)

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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.