Question: Suppose f '' is continuous on (,). (a)If f ' (1) = 0 and f '' (1) =3, what can you say about f ?

Supposef ''is continuous on (,).

(a)Iff'(1) = 0 andf''(1) =3,

what can you say aboutf?

Atx= 1,fhas a local maximum.

Atx= 1,fhas a local minimum.

Atx= 1,fhas neither a maximum nor a minimum.

More information is needed to determine iffhas a maximum or minimum atx= 1.

(b)Iff'(3) = 0 andf''(3) = 0,

what can you say aboutf?

Atx= 3,fhas a local maximum.

Atx= 3,fhas a local minimum.

Atx= 3,fhas neither a maximum nor a minimum.

More information is needed to determine iffhas a maximum or minimum atx= 3.

Supposef ''is continuous on (,).(a)Iff'(1) = 0 andf''(1) =3,what can you say

Support . " Is continuous on [-2, (). (aj w/ {) = 0 and / (1) = 3, what can you say about FF O Atx- 1, Fhas a local minimum, OMFEL, has nether a maximum nor a minimum. Hore Information Is needed to delaymine if fhas a maximum or minkran it g's (b) or (3) = 0 and / Taj = 0, what can you may shout fr Q Ari, has a local maximum. Ouxahead mamum. O at * : 3. / has neither a maximum nor a minimum. Q Hore Information Is Is determine if this a suchrum er minimum at$ 1

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