1 Suppose that the cost function for the production of a par

1. Suppose that the cost function for the production of a particular item is given by the

equation C(x) = 2x2 – 320x + 12,020, where x represents the number of items. How

many items should be produced to minimize the cost?

2. In the year 2000, Anna bought a new car for $26,000. In 2005, she was told that

the value of her car was $15,000 due to depreciation. She is told that the value of

her car depreciates linearly.

(a) Find a function V(t) which gives the value of the car t years after the year 2000.

(b) In 2008, Anna is told that she will be given $7000 for her car if she decides to

trade it in for a new car. Use the function from part (a) above to determine the

value of her car in 2008.

(c) Is the $7000 value fair based on what she was told about linear depreciation?

Explain your answer.

3. Show using Synthetic Division that x + 2 is a factor of x3 + 7x2 + x – 18.

4. In a physics experiment, it is found that the equation V(t) = 1667t – 5940t2

Expresses the velocity of an object as a function of time(t). Computer V(0.1), V(0.15), and V(0.2).

Solution

1.

C(x) = 2x^2 - 320x + 12020

d(C(x))/dt = 4x - 320

since cost should be minimize

4x - 320 = 0

x = 80

when x = 80

So 80 item should be produced to minimze the cost.