# Answer to Question #17678 in Calculus for hsd

Question #17678

MULTIPLE CHOICE QUESTION

The function f has a continuous second derivative, and it satisfies f(−1)=−3, f′(−1)=0 and f′′(−1)=1.

We can conclude that

A. f has neither a local maximum nor a local minimum at -1

B. f has a local maximum at -1

C. f has a local minimum at -1

D. We cannot determine if A, B, or C hold without more information.

The function f has a continuous second derivative, and it satisfies f(−1)=−3, f′(−1)=0 and f′′(−1)=1.

We can conclude that

A. f has neither a local maximum nor a local minimum at -1

B. f has a local maximum at -1

C. f has a local minimum at -1

D. We cannot determine if A, B, or C hold without more information.

Expert's answer

f′(−1)=0 then x=-1 can be a local extremum

f"(-1)=1>0 then f concave down so it is the pointof local minimum correct answer B

f"(-1)=1>0 then f concave down so it is the pointof local minimum correct answer B

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