Question

when the price of a certain commodity is p dollars per unit, costumers demand x hundred units of the commodity, where .5x^2 + 2px +3p^2= 249. How fast is the demand x changing with respect to time when the demand is 6 units, the price is $7 per unit and is decreasing at the rate of 10 cents per month?

Answer 1

you didnt give me a medal for my last question :/

Answer 2

ill do that right now

Answer 3

can you help me with this

Answer 4

ok lets try implicit deriv.

Answer 5

.5x^2 + 2px +3p^2= 249.

.5*2x*dx/dt + 2*dp/dt*x + 2*p*dx/dt + 3*2*p*dp/dt = 0

Answer 6

after this whats next

Answer 7

now we can plug in

Answer 8

can you tell me what to plug in

Answer 9

when the price of a certain commodity is p dollars per unit, costumers demand x hundred units of the commodity,
How fast is the demand x changing with respect to time when the demand is 6 units, the price is $7 per unit and is decreasing at the rate of 10 cents per month?

x = 6 hundred units = 600
p = 7
dp/dt = -.10


.5*2x*dx/dt + 2*dp/dt*x + 2*p*dx/dt + 3*2*p*dp/dt = 0

Answer 10

does it say demand is 6 hundred units?

Answer 11

no it say demand is 6 units

Answer 12

ok

Answer 13

lets just plug in x = 6

Answer 14

did you get 27

Answer 15

x = 6 hundred units
p = 7
dp/dt = -.10

.5*2*(6)*dx/dt + 2*(-.10)*6 + 2*7*dx/dt + 3*2*7*(-.10) = 0

Answer 16

yes I got dx/dt = .27, then multiply by 100, so 27

Answer 17

ok

Answer 18

are these answers correct ?

Answer 19

did we get the last one correct ?

Answer 20

can you help me with one more

Answer 21

need to know if we are doing them correctly

Answer 22

we are

Answer 23

ok so then the correct answer is 27