This is a parabola that opens downward.
Remember that the axis of symmetry is located at x=-b/(2a).
So the vertex is at (3,-1)
So functions slope is positive or increasing on (-co, 3] and decreasing on [3,co).
Answer:
S'(x)=-0.006x2+0.8x+9
Step-by-step explanation:
The rate of change of the sales S(x) with respect to the amount of money spent on advertising x is then the derivative of S(x) with respect to x. What we have to calculate is S'(x).
We know that the derivative of 
is 
(where a is a constant), and the derivative of a sum is the sum of the derivatives, so we can calculate the derivative of each term independently:
S'(x)=(−0.002x3 + 0.4x2 + 9x + 500)'=(−0.002)(3)x2 + (0.4)(2)x + 9
Which means:
S'(x)=-0.006x2+0.8x+9
Based on the calculations, Celine would earn a total of $65.00 assuming she delivered 10 packages.
<h3>What is a function?</h3>
A function can be defined as a mathematical expression which is used to define and represent the relationship that exists between two or more variable.
<u>Given the following function:</u>
y = 20.00 + 0.45(x)
In this exercise, you're required to determine Celine's weekly earnings based on the number of packages she delivered. However, the number of packages delivered by Celine wasn't shown, thus, we would assume a value for the purpose of an explanation:
Assuming x = 10 packages.
Substituting the value of x into the function, we have:
y = 20.00 + 0.45(10)
y = 20.00 + 45
y = $65.00.
Read more on function here: brainly.com/question/4246058
#SPJ1
