
Concept explainers
a.
To fill in the gaps: with reference to the provided graph
a.

Answer to Problem 3E
If f is increasing on an interval, then the y -values of the points on the graph increase as the x -values increase. From the graph of f , we see that f is increasing on the interval [1, 2] and [4, 5] .
Explanation of Solution
Given information: if f is increasing on an interval, then the y -values of the points on the graph____ as the x -values increase. From the graph of f , we see that f is increasing on the interval _____ and _____ .
From the provided information, consider,
As f increases the height if the function f ( x ) also increases, thus, y-values of the points on the graph increase as the x-values increase. In the graph provided, f is increasing on the intervals [1, 2] and [4, 5].
Hence, if f is increasing on an interval, then the y -values of the points on the graph increase as the x -values increase. From the graph of f , we see that f is increasing on the interval [1, 2] and [4, 5] .
b.
To fill in the gaps: with reference to the provided graph
b.

Answer to Problem 3E
If f is decreasing on an interval, then the y -values of the points on the graph decrease as the x -values increase. From the graph of f , we see that f is increasing on the interval [2, 4] and [5, 6] .
Explanation of Solution
Given information: If f is decreasing on an interval, then the y- values of the points on the graph ______ as the x -values increases. From the graph, we see that f is decreasing on the interval ____ and ____.
From the provided information, consider,
As f decreases, the height of the function f ( x ) also decreases, thus, y-values of the points on the graph decrease as the x-values increase. In the graph provided, f is increasing on the intervals [2, 3] and [5, 6].
Hence, if f is decreasing on an interval, then the y -values of the points on the graph decrease as the x -values increase. From the graph of f , we see that f is increasing on the interval [2, 4] and [5, 6] .
Chapter 2 Solutions
EBK PRECALCULUS: MATHEMATICS FOR CALCUL
- Explain how to solve all solutions of y"(x)+ay'(x)+by(x)=0 when the Characteristic Equation λ2+aλ+b=0 of the second-order linear differential equation y"(x)+ay'(x)+by(x)=0 has no real roots. Please distinguish between the two methods of "using real numbers to solve the space base" and "using complex numbers to solve the space base" and explain the key points respectively.arrow_forwardUse the circle to find exact value of each trigonometric function (number 23)arrow_forwardFind the equation of the line through (12, 11) such that the triangle bounded by this line and the axes in the first quadrant has the minimal area.arrow_forward
- Find the derivative of the function. y=8√√x+5x 6 7arrow_forwardExplain how to solve all solutions of y"(x)+ay'(x)+by(x)=0 when the Characteristic Equation λ2+aλ+b=0 of the second-order linear differential equation y"(x)+ay'(x)+by(x)=0 has no real roots. Please distinguish between the two methods of "using real numbers to solve the space base" and "using complex numbers to solve the space base" and explain the key points respectively.arrow_forwardUse the circle to find exact value of each trigonometric function (number 16)arrow_forward
- Use the circle to find exact value of each trigonometric function (number 22)arrow_forwardUse the circle to find exact value of each trigonometric function (number 20)arrow_forwardWrite an equation for the function graphed below. The y intercept is at (0,-0.2) 5+ 4 -7 -6 -5 -4 -3 3. -2- 2 1 + 1 2 3 5 6 7 -1 2 -4 3 4 5 -5arrow_forward
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning





