A model for the US average price of a pound of white sugar from 1993 to 2003 is

Question

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 - 0.04458t + 0.4074 where t is measured in years since August of 1993. Estimate the times when sugar was cheapest and most expensive during the period 1993-2003.

I know that I need to take the derivative, and have done that, and I have the answers. I need to know how to solve the derivative below for t, so that I can find the critical points.  Please show all work on how to sove for "t".

S'(T) = -0.00016185t^4 + 0.0036148t^3 -0.026868t^2 + 0.07258t - 0.04458

Explanation / Answer

You'll need to find critical points by taking the derivative of S(t) with respect to t and setting that equal to zero and solving.

Once you have your critical numbers:
0.857416
4.6066
7.30607
9.56418

you know that the max and min of S(t) has to occur at one of these or the end points of your interval (which will be 0 and 10).

So all that's left to do is plug each of these values into your original function S(t) and find which is the largest and which is the smallest.

The max should be at 4.6066 years corresponding to $0.417331 per pound
and the min should be at 0.857416 years corresponding to $0.371906 per pound.

But double check just to be sure.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.