Consider the following. x2 f(x) D x2 + 4 (a) State the domain of the function. O all real numbers x except x = -2 O all real numbers x except x = 4 all real numbers x O all real numbers x except x = 2 O all real numbers x except x = -2 and x = 2 (b) Identify all intercepts. (If an answer does not exist, enter DNE.) x-intercept (х, у) 3D y-intercept (х, у) %3D (c) Find any vertical and horizontal asymptotes. (Enter your answers as a comma-separated list of equatie

Q: Let h(x) = f(x)g(x). If f(x) = -3x²+2x 3 and g(x) 3x" + 4x + 3, what is h' (1)? Do not include "h'…

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Q: The domain of the function 15z + 7 is Z-1 S(z) = f(x) O R-(7} O R-(15} O R-(1} O R-(0} OR

A: f(x) = 15x+7x-1Denominator is x-1;if x=1then Denominator is 0.10 is not defined.

Q: f(x) = x - 6x + 9x – 6 For this function, on [-1,5] interval, the absolute maximum is 10 and the…

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Q: Find the absolute maximum and minimum values of the function f(x) = r'-6r +3 on the interval [-1,…

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Q: Locate the absolute extrema of the function f(x)=-2r+ 12x+ 3 on the closed interval [-6, 6].

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Q: What are the domain and range of the real-valued function f(x) = - 2 + yx + 7? O a. The domain is x…

A: Given f(x)=-2+x+7

Q: The absolute Extrema of the function f(x) = /-x²+ 8x - 15 on its domain are

A: Given,f(x)=-x2+8x-15

Q: Let h(x)=f(x)g(x) where f(x)=−4x^2−5x+1, g(1)=−5, and g′(1)=−4 what is h′(1)?

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Q: 1. The function f(x) "2x2 + 10x models the height above the ground, in %3D cm, of a jumping frog…

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Q: 4x+7 1<x<2 (ii) If f(x)=< [4x² – 1 determine whether the function f(x) is continuous 2<x<4…

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Q: Find the domain of the function. 29) f (x) = v25 – x2 30) f (x) = 3x + 4 31) h(x) 32) h(t) = |t + 1|…

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Q: 1. Find the domain of the following functions. f(x) = Vx2 – 9 + V16 – x2 a. b. f(x) = x2-25 1,

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Q: The domain of the function f(x)=√12+4x−x^2 is the closed interval [A,B] where A= and B=

A: Domain is the set of all values that can be taken by x so that the equation is defined.

Q: Find the absolute maximum and minimum of the function f (x) = x³ - x+2 on the interval [0, 3] %D

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Q: 1. For the function f(x) = 3x² - 5x +7 find: a. f(-2) %3D b. f(-a)

A: Please see the below picture for detailed solution.

Q: 5. The coordinates of the hole for the function f (x) x²-4 are: x-2

A: Given function, f(x)=x2-4x-2

Q: b) For the functions f(x) g(x) = 1. The length of the line through the y-intercept of g(x) and the…

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Q: Consider the function y = (x) where f(x) = x³ +2x2 - 4x and g(x) = x2 + 2. Determine a) the domain…

A: The domain of definition of a function is a set of those values for which we can define a function.…

Q: 1. Consider the function f(x) = -x² – 4x – 3 a) Determine f(-4), f(a), and f(a+ h).

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Q: The domain of the function f(x) 26 is all real numbers x except for a where z equals %3D 2x - 30

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Q: 2 For the function f(x) = -x', find f'"(x), f'"(0), f'"(1), and f"(- 1).

A: To find the double derivative for the given function.

Q: 1. How many non-real zeros does the function f(x) = x - 2x + 8x-16x have? 1. 0 2. 2 3. 3 4. 4

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Q: 3. Find the domain of the following functions: 2x+1 (a) f(x) = (b) g(x) = (c) h(x) = V4 -x+ Vx2 – 1…

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Q: 22 The domain of the function f(x) : is all real numbers æ except for a where a equals 10x – 24

A: Given : fx = 2210x - 24

Q: 22. Find the "natural" domain of the function f(x)=16r +Vx. x'-16x

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Q: 3. Determine whether x = 2 is the x coordinate of an extremum of this function: %3D f(x) =- 1 x³ +…

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Q: 20.) Find function the Ceroes algebraically. of the f(x) = x² - 6x +8 4x X = ?

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Q: 3. For the function f (x) = 4x2 – 25, a) find f(-1) - %3D %3D b) find all x when f (x) = 0

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Q: ) Given the function f(x) = {6 − x        if − 1 ≤ x ≤ 2…

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Q: f(x) = x3 -3x2 - 3x +1 x=-1 is a root of the function how would you show that?

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Q: Consider the compound function:             (x - 2)3 for x less than or equal to 2 h(x) =  |x| for…

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Q: (-2x² – 5x + 14,x 3 x= 3 continuous at x = 3. Justify the conclusion.

A: For given function f(x) ; -2x2 -  5x  + 14  , x &lt; 3   .... (i) 19  , x = 3         ..... (ii)…

Q: Question in Image.

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Q: What are the x-intercept and y-intercept of the function f(x) = 14I14? O The x-intercept is at (-2,…

A: The x- intercept is at (-2,0). There isn't a y- intercept.

Q: (a) By sketching the graph of the function f(x) = x³ + x² – 1, show that the equation f (x) = 0 has…

A: The root of the equation is 0.755 Also it is evident that it is lying between 0 and 1

Q: Find the absolute maximum and minimum values of the function over the indicated interval, and…

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Q: FOR WHAT VALUE OF X does the function g(x) = (x2-4)2 attain the absolute maximum?   X=-1 X=0…

A: We have to find for what value x the function g(x) will obtain a maximum value

Q: Find (f-g)(x) if f(x)=sqrt16x4 and g(x)=3x3-3x-5. Choose from the answers below.…

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Q: 7. Find the domain of the functions. a. g(x) = 4 +x – V3 – 5x. 7x3-x²+16 b. f(x) х2-21х-100 In(7-3x)…

A: 7 a Given function is : gx=4+x-3-5x For function gx to be defined if , 3-5x≥0-5x≥-3x≤35   Thus , the…

Q: 6- For the function f(x)=3(2x+1)(1-x²)²,Determine: a- The degree of the function b- The value of the…

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Q: Where is the function undefined and where is it equal to 0. f(x)=3e^2x-3

A: We can solve above question both through algebra and also through drawing it's graph. Both of them…

Q: 8. For the function f(x)=3x+5-11, find the values of x such that f(x)=0.

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Q: Find the X-coordinate of the points of intersection of the graphs of two functions. f (x) = x² – 11x…

A: Find the x-coordinate of the points of intersection of the graphs of two functions.…

Q: Find the absolute extrema of the function g(x) = -10x/x^2+9 on the interval (-5,2)

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Q: 10. Find the domain of the function. a) f(x) = V49 – x2

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Q: The absolute Extrema of the function f(r) = -V-x² + 8x- 15 on its domain are .2

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Q: Let h(x)=f(x)/g(x) where f(x)=x^2+5x−1, g(2)=−4, and g′(2)=−2 what is h′(2)?

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Q: V. Find the value of k that makes the function continuous. 2x2-3-15 if x + 3 if x = 3 f(x) = %3D x-3…

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Q: B. m(x) = D. h(x) = x+2 x²-4 28. What is the removable discontinuity of x²-4 the function f(x) : = ?…

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Q: The zeros of the function f(x)=x'-9x are 1) 9, only 2) 0 and 9 3) 0 and 3, only 4) -3, 0, and 3

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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.