Check Your Understanding 4.3 1. Differentiate te EXERCISES 4.3 Differentiate the following functions. 1. f(x) = ²x+3 2. f(x)=-3x-2 3. f(x) = 4x²-x 4. f(x) = (1+x)³ 5. f(x) = e 6. f(x) = et 7. f(x)=√x 8. f(x)=√1 9. f(x) = -7e7 10. f(x) = 10e 11. f(1) = 40.05 -23e9.01 12. f(t)=2e¹/2-4e0.001 13. f(1) = (²+2e)e²-1 14. f(t)=(1³-31)e¹+1 15. f(x) = (x + ¹)e²x 2. Differentiate [e³*(1 + x)]¹². 29. f(x)= 30. f(x) = 3-4x Solutions can be found following the section exercises. 4x - 1 ex/2 31. f(x)=(5x-2)e¹-2x 32. f(x) = (2x - 5)³x-1 33. An Investment Portfolio The value of an investment portfo- lio consisting of two stocks is given by f(t) = 3e0.061 +2e0.021 where it is the number of years since the inception of the port- folio, and f(t) is in thousands of dollars. (a) What is the initial dollar amount invested? (b) What is the value of the portfolio after 5 years? (c) At what rate is the investment appreciating after 5 years? 34. Depreciation of Assets The value of a computer years after purchase is v(t) = 2000e 0.35 dollars. At what rate is the com- puter's value falling after 3-years? 35. The Most Expensive Artwork to Date The highest price ever paid for an artwork at auction was for Pablo Picasso's 1955 painting Les femmes d'Alger, which fetched $179.4 million
Check Your Understanding 4.3 1. Differentiate te EXERCISES 4.3 Differentiate the following functions. 1. f(x) = ²x+3 2. f(x)=-3x-2 3. f(x) = 4x²-x 4. f(x) = (1+x)³ 5. f(x) = e 6. f(x) = et 7. f(x)=√x 8. f(x)=√1 9. f(x) = -7e7 10. f(x) = 10e 11. f(1) = 40.05 -23e9.01 12. f(t)=2e¹/2-4e0.001 13. f(1) = (²+2e)e²-1 14. f(t)=(1³-31)e¹+1 15. f(x) = (x + ¹)e²x 2. Differentiate [e³*(1 + x)]¹². 29. f(x)= 30. f(x) = 3-4x Solutions can be found following the section exercises. 4x - 1 ex/2 31. f(x)=(5x-2)e¹-2x 32. f(x) = (2x - 5)³x-1 33. An Investment Portfolio The value of an investment portfo- lio consisting of two stocks is given by f(t) = 3e0.061 +2e0.021 where it is the number of years since the inception of the port- folio, and f(t) is in thousands of dollars. (a) What is the initial dollar amount invested? (b) What is the value of the portfolio after 5 years? (c) At what rate is the investment appreciating after 5 years? 34. Depreciation of Assets The value of a computer years after purchase is v(t) = 2000e 0.35 dollars. At what rate is the com- puter's value falling after 3-years? 35. The Most Expensive Artwork to Date The highest price ever paid for an artwork at auction was for Pablo Picasso's 1955 painting Les femmes d'Alger, which fetched $179.4 million
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter3: The Derivative
Section3.CR: Chapter 3 Review
Problem 8CR
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