Question

the following function shows the relationship between the selling price (s)and profit p(s) in dollars for a company.
p(s)=-20s^2+1,400s-12,000

which statement best describes the intervals where the company profit increases decreases or records a maximum?

a.it is least when the selling price is $30

b.it is greatest when the selling price is $30

c.it decrease when the selling price increase from $10 to $35

d. it increase when the selling price increases from $10 to $35

Answer 1

@primeralph
@whpalmer4
@agent0smith
@robtobey
@e.mccormick
@douglaswinslowcooper
@Kainui
@esshotwired
@TheRealMeeeee

Answer 2

Have you tried graphing \(p(s)\) over the range of s = 10 to s = 35?

Answer 3

or even just evaluating it at s = 10, s = 30, s = 35 should give you a clue

Answer 4

i think the answer is c but im not sure

Answer 5

you could also recognize that this is a parabola and find its vertex which would give you the information to answer

Answer 6

it's good that you aren't sure about c being correct because it is not correct :-)

Answer 7

oh lol okay

Answer 8

so it must be d then

Answer 9

no need to guess, you can figure it out and know...

Answer 10

it's a parabola in the form \[y = ax^2+bx+c\]where \[a = -20, ~b = 1400, ~c=-12000\]vertex of a parabola is at \[x = -\frac{b}{2a}\]so our vertex is at \[x = -\frac{1400}{2(-20)} = \frac{1400}{40} = 35\]and because the value of \(a\) is negative, the parabola opens down and the vertex is at the maximum value of \(y\)

Answer 11

Here's a graph:

Answer 12

or if you aren't sure that's the vertex, here's a wider graph with a vertical line at s = 35

Answer 13

okay i'm for sure it's d now

Answer 14

@whpalmer4

Answer 15

thanks for your help

Answer 16

@ninjasandtigers do you know the answer to this one

Answer 17

doesn't he already have the answer? @liorafanny

Answer 18

ya nvm