Does anybody know how to solve this??
A price $p$ (in dollars) and demand $x$ for a product are related by $2x^2+2xp+50p^2=20600$.
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.
$$2x^2+2xp+50p^2=20600\tag{1}$$
$$4xx'+2x'p+2xp'+100pp'=0$$
$$x'(2x+p)+p'(x+50p)=0$$
$$x'=-{p'(x+50p) \over (2x+p)}$$
In particular instance of time:
$$x_1'=-{p_1'(x_1+50p_1) \over (2x_1+p_1)}$$
...you have the following values: $p_1'=2$, $p_1=20$. To complete the calculation you need the value of $x_1$ too. It can be obtained from (1) by solving a simple quadratic equation for $x_1$ knowing the value of $p_1$:
$$2x_1^2+2x_1p_1+(50p_1^2-20600)=0\tag{1}$$
You can proceed from here.
