Chapter 4.2, Problem 63E

To determine

To find: The time at when sugar is cheapest and most expensive.

Answer to Problem 63E

The time at when sugar is cheapest and most expensive are cheapest $t=0\cdot 855$ in June $1994$ and most expensive $t=4\cdot 618$ in march $1998$ .

Explanation of Solution

Given information:

The given function is .

Calculation:

Calculate the value of $S\text{'}\left(t\right)=0$ .

  $-0\cdot 00016185t^4+0\cdot 0036148t^3-0\cdot 026868t^2+0\cdot 007258t-0\cdot 04458=0$

On further solving the equation we get $t=0\cdot 85,4\cdot 618,7\cdot 3,9\cdot 57$ .

At $t=0\cdot 85,S\left(0\cdot 85\right)=0\cdot 3906$

At $t=4\cdot 618,S\left(4\cdot 618\right)=0\cdot 4464$

At $t=7\cdot 3,S\left(7\cdot 3\right)=0\cdot 4271$

At $t=9\cdot 57,S\left(9\cdot 57\right)=0\cdot 4365$

Out of these values at $t=0\cdot 855$ and at $t=4\cdot 618$ , the average price of sugar is vary high and low since by using extreme value theorem.

Cheapest $t=0\cdot 855$ in June $1994$ .

Most expensive $t=4\cdot 618$ in march $1998$ .

Therefore,the time at when sugar is cheapest and most expensive are cheapest $t=0\cdot 855$ in June $1994$ and most expensive $t=4\cdot 618$ in march $1998$ .