Answer to Question #17678 in Calculus for hsd

Question

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.

Answer 1

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