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

Question

(b) If f '(−4) = 0 and f ''(−4) = 0,

 what can you say about f ?

a. At x = −4, f has a local maximum.

b. At x = −4, f has a local minimum.

 c.   At x = −4, f has neither a maximum nor a minimum.

d. More information is needed to determine if f has a maximum or minimum at x = −4.

Answer 1

More info is needed.

For example, f(x) = (x+4)⁴ has a local (and absolute) min at x = -4 and f'(-4) = f"(-4) = 0

g(x) = -(x+4)⁴ has a local (and absolute) max at x = -4 and g'(-4) = g"(-4) = 0