When the price of a certain commodity is p dollars per unit, consumers demand x hundred units of the commodity, where
x^2+3px+p^2=79

How fast is the demand x changing with respect to time when the price is $ 5 per unit and is decreasing at the rate of 50 cents per month?

Question

When the price of a certain commodity is p dollars per unit, consumers demand x hundred units of the commodity, where 
x^2+3px+p^2=79

How fast is the demand x changing with respect to time when the price is $ 5 per unit and is decreasing at the rate of  50 cents per month?

anonymous · Answer

Do you know how to plug the values into the equation?

anonymous · Answer

yes

anonymous · Answer

Well first step is to plug the values in, so do that.

anonymous · Answer

so you mean p=5 ?

anonymous · Answer

yes

anonymous · Answer

so I will have x^2+15x+25=79

anonymous · Answer

I think we have to take the derivative, but i don't know how to do it! are you still there ?

dumbcow · Answer

hey, ok after plugging in p=5, you can now solve for x (the amount demanded at price of $5)
you will need that for later...but the problem says to find rate that demand is changing (dx/dt)

you need to differentiate the demand function using implicit differentiation
then plug in p=5 and dp/dt = -0.5

solve for dx/dt