1 / 20

Derivatives, Antiderivatives, and Indefinite Integrals

Derivatives, Antiderivatives, and Indefinite Integrals. Chapter Three -- Test One Review. Use the given graph of f for 1–4. f ΄ ( x ) = 0 when x = f ΄ ( x ) = 0 does not exist when x = f ΄ ( x ) < 0 when x = f ΄ ( x ) > 0 when x = Sketch f ΄ ( x ).

kermit-ruiz
Télécharger la présentation

Derivatives, Antiderivatives, and Indefinite Integrals

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Derivatives, Antiderivatives, and Indefinite Integrals Chapter Three -- Test One Review

  2. Use the given graph of f for 1–4 • f ΄(x) = 0 when x = • f ΄(x) = 0 does not exist when x = • f ΄(x) < 0 when x = • f ΄(x) > 0 when x = • Sketch f ΄(x)

  3. If f (x) = 6x2 + x-2 , then f ΄(4) =

  4. If f (x) = 6x1/3 + 8x-1/4 + 8 , then f ΄(x) =

  5. Given f (x) = 3x2 – 4x + 2 , • State f ΄(x) = • Use a definition to prove.

  6. If f (x) = -3x4 + 8x5/4 , then

  7. Sketch the graph of f (x) = 2x3 + 4x2 – 4x – 2and f ΄(x).

  8. If f (x) = 2x3 + 4x2 – 4x – 2 • Find f ΄(x)

  9. If f (x) = 2x3 + 4x2 – 4x – 2 • Find the set of values of x for which f ΄(x) = 0 are

  10. If f (x) = 2x3 + 4x2 – 4x – 2 • Determine where f (x) is increasing.

  11. If f (x) = 2x3 + 4x2 – 4x – 2 • Determine where f ΄(x) is negative.

  12. If f (x) = 2x3 + 4x2 – 4x – 2 • State the ordered pair for all local extrema of f (x). Justify your answer with calculus.

  13. Let x(t) = 4t3 – 16t2 + 12t t  0 • Determine the velocity of the particle at time t.

  14. Let x(t) = 4t3 – 16t2 + 12t t  0 • Determine the acceleration of the particle at time t.

  15. Let x(t) = 4t3 – 16t2 + 12t t  0 • Is the particle speeding up or slowing downat t = 1? Explain your reasoning.

  16. Let x(t) = 4t3 – 16t2 + 12t t  0 • When is the particle at rest?

  17. Let x(t) = 4t3 – 16t2 + 12t t  0 • When is the particle moving to the right?Justify your answer.

  18. Let x(t) = 4t3 – 16t2 + 12t t  0 • Determine all local maximums and minimums of the position function.

More Related