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Continuity and Differentiability (2nd year Baccalaureate)
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Continuity and Differentiability (2nd year Baccalaureate)

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Questions and Answers

At which point does the function $f(x) = x^3 - 3x^2 - 9x + 5$ have a local maximum?

  • $x = -1$
  • $x = 3$
  • $x = 2$ (correct)
  • $x = 0$

    • What is the derivative of $f(x) = x^3 + 4x^2 + 7x - 2$?

  • $f'(x) = 3x^2 + 4x$
  • $f'(x) = 3x^2 + 4x + 7$
  • $f'(x) = 3x^2 + 8x + 7$ (correct)
  • $f'(x) = 3x^2 + 8x$

    • What is the limit of $f(x) = \frac{x^2 - 4}{x - 2}$ as $x$ approaches 2?

  • $f(2) = -\infty$
  • $f(2) = 0$
  • $f(2) = 1$ (correct)
  • $f(2)$ does not exist

    • For which value of $k$ does the function $f(x) = kx^2 - 4x - 3$ have no critical points?

    <p>$k = 1$</p> Signup and view all the answers

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