Question

A price p (in dollars) and demand x for a product are related by
2x^2+1xp+50p^2=26000.

If the price is increasing at a rate of 2 dollars per month when the price is 20 dollars, find the rate of change of the demand.

Rate of change of demand =

Answer 1

Step 1: Take the derivative of 2x^2+1xp+50p^2=26000
d/dt(2x^2+1xp+50p^2)=d/dt(26000)

Answer 2

4xx'+x'p+xp'+100pp'=0

(4x+p)x'+(x+100p)p'=0

-(x+100p)p'/(4x+p)= x'

Answer 3

Are you following?

Answer 4

p=$20

2x^2+x(20)+50(20)^2=26000

(x+60)(x-50)

so x= -60 and x =50

The value you select has to be greater than 0, so x=50

Answer 5

yes yes i am following

Answer 6

p=$20 p'=$2 per month x= 50 units

Plug these values into x'

x'=.........

Answer 7

-((50+100(20))(2))/((4(50)+(20)))= x'

x'=

Answer 8

What do you get?

Answer 9

i'll calculate

Answer 10

is that negative((50.........?

Answer 11

yep

Answer 12

look at the original function

Answer 13

x'= a negative

Answer 14

is it -18.63?

Answer 15

-18.64 actually?

Answer 16

ya. -205/11 is the exact value

Answer 17

YES!!! its correct

Answer 18

thank you very very very much

Answer 19

Welcome

Answer 20

also another thankyou for explaining it