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Test: Function analysis using derivatives

This test uses the first derivative to analyse a function. Tasks include finding critical points, intervals of increase and decrease, local extrema and absolute maximum or minimum values.

Question qty: 10
Duration in minutes: 18
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Sample questions

  • How is the derivative sign related to increasing and decreasing?
  • For f(x) = ax² + (b)x, find the critical x where f′(x) = 0.
  • On [l, u], f(x) = m(x − (r))². Find the maximum value.
  • The derivative is f′(x) = 2(x − (r)). Where is f decreasing?
  • Which sequence is appropriate when analysing a function with derivatives?
  • What extremum occurs at the vertex of f(x) = ax²?
  • Is every point where f′(x) = 0 necessarily an extremum?
  • The derivative is f′(x) = 2(x − (r)). Where is f increasing?

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