The graph below shows a company's profit f(x), in dollars, depending on the price of pencils x, in dollars, sold by the company: Graph of quadratic function f of x having x intercepts at ordered pairs negative 0, 0 and 10, 0. The vertex is at 5, 160.

Part A: What do the x-intercepts and maximum value of the graph represent? What are the intervals where the function is increasing and decreasing, and what do they represent about the sale and profit? (4 points)

Part B: What is an approximate average rate of change of the graph from x = 2 to x = 5, and what does this rate represent? (3 points)

Part C: Describe the constraints of the domain. (3 points)

In the picture attached, the graph is shown.

profit = sales - expenses

A) x-intercepts represent the price of pencils which make the profit equal to zero, that is, they are break-even points.

increasing interval: [0, 5). As the price of pencils increases, profit also increases, then sales increases faster than expenses

decreasing: (5, 10]. As the price of pencils increases, profit decreases,  then expenses increases faster than sales

B) Average rate of change of the graph from x1 = 2 to x2 = 5:

Average rate of change = [f(x2) - f(x1)]/(x2 - x1)

From the picture,

f(2) = 100 and f(5) = 160

then:

Average rate of change = [160 - 100]/(5 - 2) = 20

This represents that, on average, an increment on the profit of $20 is made for every increment of $1 on the price of the pencils

C) The lower limit is zero because a price cannot be negative.

The upper limit is the price that makes the profit equal to zero because negative profits are not desirable.

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12

f(x) = - 2/3x + 5; f(5/2)

substitute 5/2 in for x:

f(5/2) = -2/3(5/2) + 5

simplify the right side:

f(5/2) = -5/3 + 5

f(5/2) = 10/3

answer:

f(5/2) = 10/3

i hope this you!