True or false: maxima and minima

Exercise and reference answers

Questions

1. Statement is true

   No

   Statement

   Every critical point is a point of local maximum or minimum.

2. Statement is true

   Yes

   Statement

   If f ′ does not change sign at c, then c is a point of inflexion.

3. Statement is true

   Yes

   Statement

   The second derivative test needs f to be twice differentiable at c.

4. Statement is true

   No

   Statement

   f ″(c) = 0 with f ′(c) = 0 settles the question immediately.

5. Statement is true

   Yes

   Statement

   A point where f is not differentiable can still be a critical point.

Explanation