Section 2.4.

4 6f (x) x x 1. Find the derivative of the following function.

Use the product rule.

2. Find the derivative of the following function. f (x) = x 2 (x 3 + 3)

Use the product rule.

3. Find the derivative of the following function. f (x) = √x (6x + 2)

Use the product rule.

4. Find the derivative of the following function. f (x) = (x 2 + x) (3x + 1)

Use the product rule.

5. Find the derivative of the following function. f (x) = (2x 2 + 1) (1 - x)

Use the product rule.

f (t) 6t4

3 (3t2

3 1)6. Find the derivative of the following function.

Use the product rule.

Use the product rule.

7. Find the derivative of the following function. f (x) = (x 4 + x 2 + 1) (x 3 - 3)

x 8

x 28. Find the derivative of the following function.

Use the quotient rule.

f (x) x 4 1x 3

Use the quotient rule.

9. Find the derivative of the following function.

f (x) 3x 12 x

10. Find the derivative of the following function.

Use the quotient rule.

f (s) s3 1s111. Find the derivative of the following function.

Use the quotient rule.

f (x) x 4 x 2 1x 2 1

12. Find the derivative of the following function.

Use the quotient rule.

13. Economics: Marginal Average Revenue Use the Quotient Rule to find a generalexpression for the marginal average revenue. That is calculate

and simplify your answer.

d

dx[R(x)

x]

14. Environmental Science: Water Purification If the cost of purifying a gallon of waterto a purify of x percent is for ( 50 x 100)

a.Find the instantaneous rate of change of the cost with respect to purity.b.Evaluate this rate of change for a purity of 95% and interpret your answer.c.Evaluate this rate of change for a purity of 98% and interpret your answer

C(x) 100

100 x

15. Environmental Science: Water Purification (14 continued) a.Use a graphing calculator to graph the cost function C(x) from exercise14 on the window [50,100] by [0,20]. TRACE along the curve to see how rapidlycosts increase for purity (x-coordinate) increasing from 50 to near 100.

b. To check your answer to 14, use the “dy/dx” or SLOPE feature of your calculatorto find the slope of the cost curve at x = 95 and x = 98, The resulting rates of changeof the cost should agree with your answer to Exercise 14(b) and (c). Note thatfurther purification becomes increasingly expensive at higher purity levels.

16. Business: Marginal Average Cost A company can produce LCD digital alarm clocks at a cost of $6 each while fixed costs are $45. Therefore, the company’s cost function C(x) = 6x+45.

a.Find the average cost function .b.Find the marginal average cost function.c.Evaluate marginal average cost function at x =3 and interpret your answer.

17. General: Body Temperature If a person;s temperature after x hours of strenuousexercise is T (x) = x 3 (4 – x 2) + 98.6 degrees Fahrenheit for (0 x 2), find the rate of change of the temperature after 1 hour.

18. General: Body Temperature (17 continued)

a.Graph the temperature function T(x) goven in 17, on the window [0,2] by [90, 110].TRACE along the temperature curve to see how the temperature rises and falls as time increases

b. To check you answer to 17, use the “dy/dx” or SLOPE feature of your calculator to find the slope (rate of change) of the curve at x =1. Your answer should agree with youranswer in 17.

c. Find the the maximum temperature.