# Minimum Price?

• Apr 14th 2010, 05:08 PM
akuczma86
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?
• Apr 14th 2010, 05:10 PM
Prove It
Quote:

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?
• Apr 14th 2010, 05:12 PM