1. ## Minimum Price?

The price P of a certain computer system decreases immediately after its introduction and then increases. If the price P is estimated by the formula $\displaystyle P = 160t^2 - 1700t + 6700$, where t is the time in months from its introduction, find the time until the minimum price is reached.

First derivative of P = $\displaystyle 320t - 1700 = 0.$
$\displaystyle 320t = 1700.$
$\displaystyle t = 5.3125.$

$\displaystyle 160(5.3125)^2 - 1700(5.3125) + 6700 = 2184.375$

I've made it this far, but how do I solve for the minimum price?

2. Originally Posted by akuczma86
The price P of a certain computer system decreases immediately after its introduction and then increases. If the price P is estimated by the formula $\displaystyle P = 160t^2 - 1700t + 6700$, where t is the time in months from its introduction, find the time until the minimum price is reached.

First derivative of P = $\displaystyle 320t - 1700 = 0.$
$\displaystyle 320t = 1700.$
$\displaystyle t = 5.3125.$

$\displaystyle 160(5.3125)^2 - 1700(5.3125) + 6700 = 2184.375$

I've made it this far, but how do I solve for the minimum price?
Didn't you just do that?