The following graph shows the average American household debt h as a function of the date d. Here h(d)  epresents household debt as a percentage of disposable income.   (a) Explain the meaning of  h(1975)  in practical terms.   h(1975) is the average American household debt as a percentage of disposable income in 1975. h(1975) is the average American household debt in dollars in 1975.     h(1975) represents the year in which household debt was at its maximum value.h(1975) is the average American household debt, as a decimal, in 1975. h(1975) represents the year in which household debt was at its minimum value. Use the graph to find its value.  % (b) The graph reaches a maximum value. Estimate the maximum value.  % Estimate the year in which the maximum value occurred.

Q: The relationship between the amount of time a car is parked, in hours, and the cost of parking, in…

A:

Q: Sketch the graph of the function defined by the formula 0 , x<-1 f(x) = |1– x² ,-1<x <1 x 2 1

A: Given:     To determine: the graph of f(x)

Q: Plot five points on the graph of the function f(x)=(1/2)^x

A: f(x) = (0.5)x Because 1/2=0.5

Q: One yardstick for measuring how steadily—if slowly— athletic performance has improved is the mile…

A: Given, In 1954, Roger Bannister of Britain cracked the 4-minute mark, setting the record for running…

Q: Sketch the graph of f.

A: We have to sketch the graph of function: fx=35x Since this is exponential function therefore its…

Q: The concentration of salt x in a homemade soap maker is given as a function of time by

A:

Q: Sketch the graph of the function by first making a table of values.

A:

Q: Sketch the graph of the function, x + 1, x', х — 1, if x 2

A: Given function  f(x) = x+1,if x&lt;0x2,if 0≤x≤2x-1,if x&gt;2

Q: A cell phone plan charges $49.95 per month plus $14.02 in taxes, plus $0.40 per minute for calls…

A:

Q: Does the following represent a function?

A:

Q: On a certain route, an airline carries 7000 passengers per month, each paying $150. A market survey…

A:

Q: Select the graph of the function. f(x)=

A: Given:

Q: uppose that during the period 1990–2001, U.S. imports of pasta increased from 270 million pounds in…

A: (a) It is given that the imports of pasta in 1990 is 270 million pounds. So, the initial value is…

Q: The graph below shows a function that represents the weekly earnings, in dollars, for a company that…

A: To find: All the correct options.  Examine the graph carefully to determine the given statement is…

Q: Suppose that Px represents the percentage of income spent on health care in year xand represents…

A: Given, P(x) represents the percentage of income spent on health in year x. I(x) represents income in…

Q: On a certain route, an airline carries 7000 passengers per month, each paying $90. A market survey…

A: Given 7000 passengers per month paying $90. Each $1 decrease in the ticket price. The airline will…

Q: Find the slope of the graph of the function at the given point.

A:

Q: In 2009 the U.S. Postal Service charged $1.17 postage for first-class mail retail flats (such as an…

A: Given, Service charged is $1.17 postage for the class first weighting up to 1 ounce. And S0.17 each…

Q: billy-sean o'hagan notices that the demand for the college newspaper was 2,000 copies each week when…

A: Given The demand for the college newspaper was 2,000 copies each week when the paper was given free…

Q: The construction industry was one of the hardest-hit by the recession of 2008, but housing starts…

A: NOTE: Refresh your page if you can't see any equations. . here x= number of years after 2002 so…

Q: Sketch the graph of the function f(x)= H

A: Given,         f(x)=x2x2-x

Q: Find the slope of the graph of the function at the given point.                       f(x) = √(1 −…

A:

Q: Sketch the graph of the function defined by the formula 0, x<-1 f(x) = /1- x² ,-1< x < 1 x 2 1

A: Given function, f(x)=         0  ,           x≤-11-x2 ,      -1&lt;x&lt;1        x  ,           x≥1

Q: The education of women in Oman in the year 1999 was (30+S) percentages. It was increased to (75+R)…

A: Women education in Oman: Given: S=1 and R=5. In year 1999 - (30+S)%=31% In year 2015 - (75+R)%=80%.…

Q: Graph the accumulated empty seat miles from January 2002 to month t as a function of t, and use your…

A: From the data given by the Bureau of Transportation Statistics,  To find the accumulated empty…

Q: A cell phone plan charges $49.95 per month plus $14.02 in taxes, plus $0.40 per minute for calls…

A:

Q: The aerobic rating of a person x years old is modelled by the function A(x) = 110(In x-2) for x 2…

A: The maxima and minima can be found for the function by differentiation. For the values of maxima the…

Q: Find the point on the graph of the function that is closest to the given point.

A: To find the point on the graph of the function fx=x that is closest to the point 4,0

Q: Sketch the graph of the function.

A: the given function is: hx=5x-2 we have to sketch the graph of the given function.

Q: Sketch the graph of the function y = (1/3)x

A: we sketch the graph of the function y = (1/3)x

Q: Sketch the graph of the following functions a) X/x+2 b) 1/(x−3)2

A: We can find the graphs as below

Q: b) Write a piecewise-defined function for the income of an author (f(x)) who earns $10 for each book…

A:

Q: What is the end behavior of this following function? y

A: The graph given represents a function with even power of x and a negative constant.

Q: The graph shows the population growth of Waco, Texas. Which function best represents t 3000004…

A: consider the curve is P = A0at

Q: Sketch a graph of the function by first making a table of values. H(x) = |2x|

A: Solving this question, we start by making the table of the equation for values -3, -2, -1,0, 1, 2…

Q: Supposed that from 2020 to 2060, the number of females in the U.S. under the age of 18, in millions…

A: Given Data: The number of females in the US under 18 is: N=0.140x+36.4 The slope of the graph of the…

Q: The rate of expenditures on public elementary and secondary schools, in billions of dollars per…

A: Given query is to find total expenditure.

Q: Suppose that P(x) represents the percentage of income spent on health care in year x and I(x)…

A: To determine function H that represents total health care expenditures in year x

Q: Sketch the graph of the function. y = e−x

A: The given function is y=e-x   First we will make a table which will satisfy y=e-x

Q: sketch the graph of the function y = (1/4) x

A: Given:y=14x

Q: Assume that the growth of the membership of a country club was linear from 1996 to 2000 with a…

A: At 1996 be the starting year At 1996 x = 0 &amp; p = 742 At 1997 x = 1 &amp; p = 742 + 236 = 978 The…

Q: What is a one-to-one function?

A: A function can be said to be one-to-one if it never takes on the same value twice or more.

Q: 7. A worker gets $20/hour for a normal work week of 40 hours and time-and-a-half for overtime.…

A:

Q: What is meant by linear function in reference to algebra?

A:

Q: Sketch the graph of the function. y = csc x/2

A: We have to graph of y=csc x2 First, we will make a table of cosec x2

Q: where's the diagram for the piecewise function?

A: Given that, a computer cafe charges their customer $40 per hour.A discount of $10 will be given to a…

Q: What is the relation between the differentiability andcontinuity of a function?

A: All differentiable functions are continuous, but not all continuous functions are differentiable.

Q: The population of Boston, MA in 2019 was 692,600 people with an annual rate of increase 1.4%. In…

A: Given the function of population grows is P(x) = 692,600·1.014x where x is number of years. We have…

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.