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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 ).

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Derivatives, Antiderivatives, and Indefinite Integrals

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  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.

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