Complete the second derivative test

Exercise and reference answers

Missing parts

1. Answer

   maxima

   Choices

   1. maxima
   2. minima
   3. inflexion

2. Answer

   minima

   Choices

   1. maxima
   2. minima
   3. inflexion

3. Answer

   fails

   Choices

   1. fails
   2. still applies
   3. gives inflexion

Complete the statement

If f ′(c) = 0 and f ″(c) < 0 then c is a point of local {0}. If f ′(c) = 0 and f ″(c) > 0 then c is a point of local {1}. If f ″(c) = 0 as well, the test {2}.

Explanation