Question

Maximum-Minimum problems

Answer 1

@jim_thompson5910

Answer 2

So I get 34.25 for x and input that into p(x) and thats my answer?

Answer 3

Oh wait no no i did it wrong

Answer 4

34.25 is close, but that's a bit small

Answer 5

p(x)=7+5.7 x-0.05 x^2
Deriv of 5x=5
5=0?

Answer 6

Profit = Revenue - Cost

P(x) = R(x) - C(x)

P(x) = 5x - (0.05x^2 + 0.7x + 7)

P(x) = 5x - 0.05x^2 - 0.7x - 7

P(x) = -0.05x^2 + 4.3x - 7

P ' (x) = -0.10x + 4.3

0 = -0.10x + 4.3

x = ??

Answer 7

Lost internet. x=43

Answer 8

good, now plug that into the P(x) function

Answer 9

oh wait, they just want the number of units, not the actual profit

Answer 10

so the answer is 43

Answer 11

Hmm I'm looking at my textbook and it says something different. It says:
Set both derivs equal to each other and solve for x.

Answer 12

you set the derivative of P(x) equal to 0, then solve for x

Answer 13

not sure what you mean by "each other"

Answer 14

You get the same answer.
R'(x)=C'(x)
x=43

Answer 15

oh that makes sense because

R ' (x)=C ' (x)

R ' (x) - C ' (x) = 0

P ' (x) = 0

Answer 16

so either way works

Answer 17

http://gyazo.com/8bb5657d464f8f50909f95f79132e549

Answer 18

to answer the second part, plug x = 43 into P(x)

Answer 19

that will give you the profit if you sold 43 units

Answer 20

So for profit, it says R(x)-C(x) for x=43

Answer 21

So yes, p(x) pretty much is the same exact thing

Answer 22

I have more questions ill post a new one.