Section 2.4. 1. Find the derivative of the following function. Use the product rule.
18
Section 2.4. 4 6 f(x) x x 1. Find the derivative of the following function. Use the product rule.
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Transcript of Section 2.4. 1. Find the derivative of the following function. Use the product rule.
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.
