second derivative test: problem 2\n(1 point)\nthe function f has a continuous second derivative, and it…

second derivative test: problem 2\n(1 point)\nthe function f has a continuous second derivative, and it satisfies ( f(-6)=8 ), ( f(-6)=-3 ) and ( f(-6)=-1 ).\nwe can conclude that\no a. f has a local minimum at -6\no b. f has a local maximum at -6\no c. f has neither a local maximum nor a local minimum at -6\no d. we cannot determine if a, b, or c hold without more information.

second derivative test: problem 2\n(1 point)\nthe function f has a continuous second derivative, and it satisfies ( f(-6)=8 ), ( f(-6)=-3 ) and ( f(-6)=-1 ).\nwe can conclude that\no a. f has a local minimum at -6\no b. f has a local maximum at -6\no c. f has neither a local maximum nor a local minimum at -6\no d. we cannot determine if a, b, or c hold without more information.

Answer

Explanation:

Step1: Recall the second - derivative test

The second - derivative test states that if (f^{\prime}(c)=0) and (f^{\prime\prime}(c)>0), then (f(x)) has a local minimum at (x = c); if (f^{\prime}(c)=0) and (f^{\prime\prime}(c)<0), then (f(x)) has a local maximum at (x = c). Here, (c=-6), (f^{\prime}(-6)=- 3\neq0).

Answer:

C. (f) has neither a local maximum nor a local minimum at (-6)