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Evaluating and graphing the given functions

1. Evaluate the function f(x) = 9x - 6 for x=0.

2. Bob owns a watch repair shop. He has found that the cost of operating his shop is given by C(x) = 4x2-296x+85 , where c is cost and x is the number of watches repaired. How many watches must he repair to have the lowest cost?

3. Find the slope of the line through the points ( 5, -5) and ( 6, -1)

4. Kafka Inc. imports hard drives and sells them on the internet. The profit is given by the equation P = 140n - 8500, where n is the number of hard drives sold. Graph P = 140n - 8500 for n < 1000. Estimate the profit, to the nearest ten dollars, corresponding to the sale of 875 hard drives.

5. When $ 8500 is invested in a savings account paying simple interest for the year, the interest, i in dollars, can be obtained from the equation i = 8500r , where r is the rate of interest in decimal form. Graph i = 8500r , for r up to and including a rate of 16%. If the rate is 12%, how much interest is earned?

Solution Preview

Please refer attached file for graphs and better clarity of expressions.

1. Evaluate the function f(x) = 9x - 6 for x=0.

f(x)=9x-6
f(0)=9*0-6=3

2. Bob owns a watch repair shop. He has found that the cost of operating his shop is given by C(x) = 4x2-296x+85 , where c is cost and x is the number of watches repaired. How many watches must he repair to have the lowest cost?

C(x)=4x^2-296x+85
Differentiate with respect to x, we get
C'(x)=8x-296
Put C'(x)=0
8x-296=0
x=296/8=37

Let us find second derivative of C(x)
C''(x)=8

We find that it ...

Solution Summary

There are five problems. Solutions to these problems explain the steps to evaluate and graph the given functions. Solutions also explain the methodology to find the slope of a line passing through the two given points.

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