(a) Find the intervals of increase or decrease.(b) Find the local maximum and minimum values.(c) Find the intervals of concavity and the inflection points.(d) Use the information from parts (a)–(c) to sketch the graph.Check your work with a graphing device if you have one.   f(x) = 2 + 2x2 - x4

Q: Consider the function y = 2/x+2+4. what are the domain and range of the function? Show your work.

A: Given query is to find the domain and range of the function.

Q: 2. f(x) = (50.9)-* + 137 (instruction: take x = - 1.50, - 1.00, - 0.50, 0, 0.50, 1.00, 1.50)

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Q: 2) y=-5+ Vx+ 1

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Q: Graph the function : y= f(x)=, - 2x² + 3x + 2 3

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Q: Find the value of the graph of f(x) = -x² + 4 between x = -5 and x = 2

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Q: 4. Given the function fx)={x+3} -5 complete the following: a) Graph f(x). (1.5A) b) Write an…

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Q: Sub parts  e. , f. , and g.

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Q: Explain why g(x) = across the y-axis, or by shifting the graph of f one unit to the right and…

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Q: 31. Sketch a graph of f(x)= x³ +7x² +8x-16. Identify the x- and y-intercepts of your graph.

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Q: Consider the equation y=x^3-16x^2+2x-4 a. Determine all intervals over which the graph is concave…

A: For a function y = f( x ) For concave up f''( x ) > 0 For concave down f''( x ) < 0  Given…

Q: Use the x-intercepts to find the intervals on which the graph of f is above and below the x-axis. 7)…

A: we need to find out the intervals where function is below the x-axis and above the x-axis.

Q: B- Find the Domain, Range and Sketch the graph of the function y = 2cos(x-

A: Given y=2cosx-π3

Q: Explain how each graph is obtained from the graph of y = Fx). (a) y = fx) + 8 O Shift the graph 8…

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Q: 5. A point on the graph of y=f(x) is (-2, 7). The corresponding point graph of y=f(2x) is: on the

A: Graph : y=fxCoordinate : -2, 7

Q: Find domain and the range of each function. S(x,y) =4x² + y 1. f(x.y) =/9- x* - y² 2.

A: (1) the domain of the function, f(x,y) = 4x² + y² is, R×R , or, R²    since, 4x² + y² ≥ 0, for all…

Q: The multiplicity of the root r= of f(x) = 1+cos(2x) is A Not a root! B None of the above. © 1 D E

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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.