The second derivative test

Exercise and reference answers

Questions

1. Question

   f ′(c) = 0 and f ″(c) < 0 means

   Choices

   1. local maximum
   2. local minimum
   3. inflexion

   Correct choice

   local maximum

2. Question

   f ′(c) = 0 and f ″(c) > 0 means

   Choices

   1. local maximum
   2. local minimum
   3. no conclusion

   Correct choice

   local minimum

3. Question

   f ′(c) = 0 and f ″(c) = 0 means

   Choices

   1. local maximum
   2. local minimum
   3. the test fails

   Correct choice

   the test fails

4. Question

   When the second derivative test fails you should

   Choices

   1. go back to the first derivative test
   2. declare no extremum
   3. differentiate a third time

   Correct choice

   go back to the first derivative test

Explanation