Question

The per-copy cost of printing, marketing, and shipping x million copies of Danielle Tinne's new novel is given by the formula
C(x)=753-225x+3x^3
Find the number of copies that lead to the lower cost per copy, and find that minimum cost.

Answer 1

@AccessDenied @Whiterabbit541 @danielbarriosr1 @francesco.alemanno PLEASE HELP ME

Answer 2

straightforward problem,
find the derivative and set it equal to 0

Answer 3

how do i do that. Can you show me step by step

Answer 4

know how to take derivative of a function ?

Answer 5

can i switch the numbers around like 3x^3-225x+753

Answer 6

definitely :)

Answer 7

Okay so C(x)=\[3x^3-225x+753\]

Answer 8

the derivative is 9x^2-225

Answer 9

@rational

Answer 10

excellent ! set it equal to 0
and solve x

Answer 11

9x^2-225=0

Answer 12

wait how do i solve for x if theres an exponent

Answer 13

first cancel out 9

Answer 14

9x^2 - 225 = 0

9(x^2 - 25) = 0


x^2 - 25 = 0

Answer 15

x^2 = 25

x = ?

Answer 16

isnt it suppose to be 225
where did you got 25?

Answer 17

@rational

Answer 18

I have factored out 9 from 225 :

225 = 9*25

Answer 19

and what happens to the 9?? you just take it out?

Answer 20

Alright, forget about my earlier work

Answer 21

Here is another way to simplify :

9x^2 - 225 = 0

9x^2 = 225

x^2 = 225/9

Answer 22

whats the value of 225/9 ?

Answer 23

whats the value of 225/9 ?

Answer 24

5

Answer 25

now we need to find the minimum cost

Answer 26

yes minimum value occurs at x = 5

Answer 27

But whats the minumum cost? thats the question

Answer 28

To get the minimum cost,
evaluate the given function at x = 5

Answer 29

C(x)=753-225x+3x^3

C(5) = ?

Answer 30

from the original function or the derivative

Answer 31

from the original function only.

the job of derivative is over. it just tells u where the minimum/maximum value OCCURS.

Answer 32

minimum cost is 3

Answer 33

to get the minimum/maximum value, u need to evaluate the original given function

Answer 34

3 is correct !

Answer 35

so, for minimum cost she needs to make 5 million copies
and the minimum cost is 3 whatever unit it is