5. The function f(x) = 2.75x2 models the packaging costs, in cents, for shipping a book with the side lengths, in inches, shown in the diagram. What are reasonable domain and range values for this function? %3D A domain: 4 4; range: f(x) > 44 © domain: 4 < x < 12; range: 44 < f(x) < 396 D domain: x> 0; range: f(x) > 0

Q: A cat is falling from a branch. Its height t seconds after it fell is given by the function h(t) =…

A: We have given height  ht=-16t2+5 To get for what height cat was falling  Put t=0 h0=0+5 h0=5 height…

Q: If the function is defined as gx=3x^2 -5(x+2), what is the value of g(4)

A: Given, gx = 3x2 -5x+2   We have to find the value of g4

Q: graph f(x)=(x-3)^2

A: To graph f(x)=(x-3)2.

Q: Evaluate (f−g)(x) f(x)=x^2+5x+2 g(x)=4x−2

A:

Q: Consider the following.   f(x) = (x^3+3x^2+x-8)/x   Rewrite the function by dividing each term of…

A: Given,

Q: is f(x)=3x^3-6 a one to one function if not what are the x values

A: Yes. Given function is one to one function.

Q: ia f(x) = x^2 - 9 a one to one function

A:

Q: Find g(1) if g(x)=x^2+1

A:

Q: find and simplify F(x)= x^2/x-7 F(4x)

A:

Q: f(x)

A: Please refer to the image below

Q: Describe the end behavior of this function f(x)=(x^3)-(4x^2)+6

A:

Q: Define the graph of the function f(x) = x^2?

A: fx=x2 x f(x) 0 0 1 1 2 4 -1 1 -2 4

Q: Neglecting air​ resistance, the distance, s(t) in feet traveled by a freely falling object is given…

A:

Q: What does the 5 represent in the function f(x)=5(2)^x?

A: Explanation of the answer is as follows

Q: Find the inverse function of f^-1 of the function. F(x) = 5sinx-7

A:

Q: Differentiate f(x)=(3x^2-6)^5

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.