Sketch the graph of a function f that is defined over all real numbers and that is decreasing on the interval [-2,3], concave down on the interval (-2, 2), and concave up on the interval (2, 3).

Q: What is the definition of the piecewise function from the given domain and range: Domain: (-…

A: The domain and range is given as , Domain = (-∞,0]∪2,∞ Range = -∞,4 find the definition of piecewise…

Q: The one-to-one functions g and h are defined as follows. g = {(-7, -4), (2, 6), (3, 9), (6, 0)} h(x)…

A: The solution of the problem is given in the next steps.

Q: A function and its graph are given. Fx) = + 4x - 20x - 20 250 200 150 100 50 -10 -5 - 50 (a) From…

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Q: Find the domain of the composite function f-g. 1) f(x) · g(x) = x+91 45 X+5 A) (xx-5, x-10) C)…

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Q: What is the domain in interval notation of the function scrt(x-4)/scrt(x-6)

A: Solution:function :- x-4x-6∵we know that the value in the square root can not be…

Q: Determine the end (long run) behavior for the function below: f(x) = x - 3x³ + x – 1 Select the…

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Q: What is the range of the function g(t)=t^2 - 5 when the domain is defined as the set of integers, t,…

A: Find the range

Q: With a function of x^4 - 50x^2 + 9, and  increasing intervals at [-5, 0] and [5, infinity), and…

A: To find the inflection points of the given functions.

Q: Find the interval in which the following function is decreasing: 3 -1 1 -1 -2 -3

A: A function f is said to be increasing  if f(x1)<f(x2) for x1<x2 and x1,x2 belonging to the…

Q: List the intervals on which f is decreasing

A: From the given graph, it is observed that the graph of the function f increasing in the intervals…

Q: (-19, 13) (10, 1) (0, -15) (12, 20) (7, -14) (12, 14) (12, -18) (15, -18) (15, -4) (5, 2) (5, 10)…

A: we have to check which is function or not

Q: f(xh) fx) - , h 0, for the given function f Find the difference quotient h f(x) _

A: The given function is:

Q: Find an equation for the graph sketched below -5 -4 -3 -2 -1 ƒ(x) = 8 7 6 5 4 3 2 7 -1 -2 -3 A -5 -6…

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Q: h(x) 36千 27 18- 9- -5 -4 3-2 -i 0/1 2 4 5-x 3 4 6- -18+ 27+ 36+ -45+

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Q: x+ if -5 <I< 2 1. Sketch the graph of f(x) 글고+ if 2 <n<5 2. Note that f(2) is a one-to-one function.…

A: Solution:-

Q: Suppose f is a 1-1 function and f-1 (4) = 7.  a) What is f(7)? b) Evaluate (f^−1 ∘ ?)(5). c) If…

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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.