supply function

Question

The supply function for a product is given by p=75+100√(4x+5), where xx is the number of units supplied and p is the price in dollars. If the price is increasing at a rate of $1 per month, at what rate is the supply changing when x=19?

Answer 1

dp/dt = 200/(4x + 5)^1/2·dx/dt; dx/dt = (4x + 5)^1/2·dp/dt/200 = (86 + 5)^1/2·1/200 = 0.045 unit per month