Section 2.4. 1. Find the derivative of the following function.

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Presentation transcript:

Section 2.4. 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 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 5. Find the derivative of the following function. f (x) = (2x 2 + 1) (1 - x) Use the product rule.

6. Find the derivative of the following function. Use the product rule.

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

8. Find the derivative of the following function. Use the quotient rule.

9. Find the derivative of the following function. Use the quotient rule.

10. Find the derivative of the following function. Use the quotient rule.

11. Find the derivative of the following function. Use the quotient rule.

12. Find the derivative of the following function. Use the quotient rule.

13. Economics: Marginal Average Revenue Use the Quotient Rule to find a general expression for the marginal average revenue. That is calculate and simplify your answer.

14. Environmental Science: Water Purification If the cost of purifying a gallon of water to a purify of x percent is for ( 50  x 100) Find the instantaneous rate of change of the cost with respect to purity. Evaluate this rate of change for a purity of 95% and interpret your answer. Evaluate this rate of change for a purity of 98% and interpret your answer

15. Environmental Science: Water Purification (14 continued) Use a graphing calculator to graph the cost function C(x) from exercise 14 on the window [50,100] by [0,20]. TRACE along the curve to see how rapidly costs 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 calculator to find the slope of the cost curve at x = 95 and x = 98, The resulting rates of change of the cost should agree with your answer to Exercise 14(b) and (c). Note that further 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. Find the average cost function . Find the marginal average cost function. 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 strenuous exercise 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) 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 your answer in 17. c. Find the the maximum temperature.