Question

The cost of controlling emissions at a firm rises rapidly as the amount of emissions reduced increases. Here is a possible model:
C(q) = 4,900 + 96q2
where q is the reduction in emissions (in pounds of pollutant per day) and C is the daily cost to the firm (in dollars) of this reduction. What level of reduction corresponds to the lowest average cost per pound of pollutant? (Round your answer to two decimal places.)
pounds of pollutant per day

What would be the resulting average cost to the nearest dollar?
$ per pound

Answer 1

the lowest would be you minimum the way you know it
when you studied parabolas

Answer 2

Do you know how to find the minimum or maximum?
well in this case it is a minimum since 96 is positive

Answer 3

yea i think so! dont i just find the derivative and then set it equal to 0 and then plug back in?

Answer 4

eh you learned about derivatives
okay you need to find critical points
find the min and plug it in
you a pretty good idea here^_^

Answer 5

I thought the question was given to you in precalc

Answer 6

no its business calc

Answer 7

it is the same thing! just you lecture focuses on business models

Answer 8

so i find the derivative then = 0 right?

Answer 9

yep! now go for it

Answer 10

i got 0

Answer 11

192q for the deriv and then =0 and i got 0??

Answer 12

yes you should get f'(0)=0

Answer 13

c'(q) i mean

Answer 14

so thats my answer?

Answer 15

no!

Answer 16

or what do i have to do next?

Answer 17

that's just a critical point! you need to find if it is min or not

Answer 18

you need to check if the derivative changes the sign left of 0 and right of 0
if not that wouldn't be a min

Answer 19

well obviously left of zero the derivative is always negative
and right of zero it is positive so
f(0) is a minimum

Answer 20

its a min

Answer 21

right!

Answer 22

f(0) not 0

Answer 23

yes we have a min

Answer 24

so whats next?

Answer 25

f(0) find the value?

Answer 26

isnt it just 4900?

Answer 27

yes!

Answer 28

okay...

Answer 29

the level of reduction is 0
the lowest average that corresponds to that is 4900

Answer 30

you are in good shape to go

Answer 31

it says its wrong?

Answer 32

eh! let met reread the problem

Answer 33

mmkay

Answer 34

anything?

Answer 35

I'm graphing it!

Answer 36

okay its okay! i actually have to leave to work in a few minutes so ill try and figure it out later:/

Answer 37

eh okay
i think you need to solve c(q)=0

Answer 38

good luck

Answer 39

thank you!

Answer 40

welcome