Suppose f '' is continuous on (−∞, ∞).

Question

(a) If f '(−5) = 0 and f ''(−5) = −3,

 what can you say about f ?

a. At x = −5, f has a local maximum.

b. At x = −5, f has a local minimum.

  c. At x = −5, f has neither a maximum nor a minimum.

d. More information is needed to determine if f has a maximum or minimum at x = −5.

Answer 1

There is a test for concavity and the second derivative. Use it.