1. ## optimazation problem

a model for the us average price of a pound of white sugar from 1993 to 2003 is given by the function S(t)= -0.00003237t^5 + 0.0009037t^4 -0.008956t^3 + 0.03629t^2 + 0.4074 where t is measured in years since August of 1993. estimate the times which sugar was cheapest and most expensive during the decade from 1993 to 2003,

I know i need to take the derivative and find the critical points but i am having a hard time setting the derivative to zero

2. Originally Posted by flashdawg
a model for the us average price of a pound of white sugar from 1993 to 2003 is given by the function S(t)= -0.00003237t^5 + 0.0009037t^4 -0.008956t^3 + 0.03629t^2 + 0.4074 where t is measured in years since August of 1993. estimate the times which sugar was cheapest and most expensive during the decade from 1993 to 2003,

I know i need to take the derivative and find the critical points but i am having a hard time setting the derivative to zero

The maximum (minimum) of a function on an interval will be a calculus type extremum in the interval or occur at an end point of the interval.

What do you have for the derivative?

You will notice that t=0 is one root, so take out t to leave you with a cubic. Plot the cubic to see where ther roots if any are between 0 and 10, you may find that there are no further roots in the given range.

So you have a calculus like extremum at t=0, and there will be another maximum or minimum at the other end of the interval.

So calculate S(0) and S(10) the smaller will be the global minimum of S in the interval and the larger will be the global maximum in the interval.

Finally you might just as well have plotted S(t) for t between 0 and 10 anyway.

CB