by **barnamah** » Fri 08 April, 2011 18:36

fort the first question of the sales `p(x) = 100 - 0.002x^2` find the rate of change when sales are at 9407

First find the derivatives of the `p(x) = 100 - 0.002x^2`

`(dp)/dx=2(-0.002)x^(2-1)=-0.004x`

so we have our equation rate as `p'=0.004x` to find the rate when x= 9407 we sub it into the equation

`p'=-0.004(9407)=-37.638` so it is decreasing

Question 2

for the 2nd question ` p(x) = 971 - 3x^2` find `(dR)/dt` if `dx/dt = 7` when x = 2.4.

the question asks for `(dR)/dt` and it is `(dR)/dt=(dR)/dx*(dx)/dt`

We have to find `(dR)/dx` which means take the derivative of the ` p(x) = 971 - 3x^2`

`(dR)/dx=-6x`

and we have `dx/dt = 7`. in our formula `(dR)/dt=(dR)/dx*(dx)/dt` sub in the values and we have:

`(dR)/dt=-6x*7=-42x`

so `(dR)/dt=-42x`

Explore and know. That is asked.