A price p (in dollars) and demand x for a product are related by

Question

A price p (in dollars) and demand x for a product are related by

2x^2−10xp+50p^2=6200.

If the price is increasing at a rate of 2 dollars per month when the price is 10 dollars, find the rate of change of the demand.

Rate of change of demand =

Answer 1

We know when p=10, dp/dt = 2 from the questions.

We need dx/dt when p=10

So differentiate implicitly (wrt t)

2x dx/dt - 10x dp/dt - 10p dx/dt + 100p dp/dt = 0

When p = 10, 2x² -100x + 5000 = 6200

2x² - 100 x - 1200 = 0

You can solve this for x.

Then substitute x, dp/dt, p into the above equation and solve for dx/dt.