The answer is b, f(x) = (x) + 1.
Answer:
dy/dt = y ( 3 - y )
Step-by-step explanation:
Given data:
Determine an autonomous differential equation with the following properties
y = 0 and Y = 3
y' > 0 for 0 < y < 3
y' < 0 for -∞ < y < 0 and 3 < y < ∞
considering an autonomous differential equation
dy/dt = y ( 3 - y )
y = 0 and 3 represents equilibrium solutions
if 0 < y < 3 then y ( 3 - y ) > 0 for 0 < y < 3
hence : dy / dt = y' > 0 for 0 < y < 3
y ( 3 - y ) < 0 for -∞ < y < 0 and 3 < y < ∞
hence : dy / dt = y' < 0 for -∞ < y < 0 and 3 < y < ∞
this shows that the autonomous differential equation satisfies every condition hence the autonomous differential equation is :
dy/dt = y ( 3 - y )
Difference quotient = [f(x+h) - f(x)]/h
[-5(x+h) -3 - (-5x -3)]/h
[-5x -5h -3 + 5x +3]/h
[-5h]/h
-5
A number line was used to draw and label a figure for Points X and Y that lies on CD as shown in the image attached below.
<h3>What is a line segment?</h3>
A line segment can be defined as the part of a line in a geometric figure such as a triangle, circle, quadrilateral, etc., that is bounded by two (2) distinct points and it typically has a fixed length.
<h3>What is a number line?</h3>
A number line can be defined as a type of graph with a graduated straight line which contains numerical values (positive and negative numbers) that are placed at equal intervals along its length.
A number line would be used to draw and label a figure for Points X and Y that lies on CD as shown in the image attached below.
Read more on collinear points and segment here: brainly.com/question/3307641
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