Two are true, one is not

Exercise and reference answers

Questions

1. False statement

   f ′(c) = 0 and f ″(c) = 0 gives a local maximum

   Statements

   1. f ′(c) = 0 and f ″(c) < 0 gives a local maximum
   2. f ′(c) = 0 and f ″(c) > 0 gives a local minimum
   3. f ′(c) = 0 and f ″(c) = 0 gives a local maximum

2. False statement

   Every critical point is a local extremum

   Statements

   1. Every critical point is a local extremum
   2. A critical point may be a point where f is not differentiable
   3. f ′(x) ≥ 0 on an interval means f is increasing there

3. False statement

   The working rule ignores the endpoints

   Statements

   1. The absolute maximum may occur at an endpoint
   2. The working rule ignores the endpoints
   3. The working rule evaluates f at critical points and endpoints

Explanation