predicting key aspects using a table x -4 -3 -2 -1 0 1 2 3 4 f(x) -54 -20 -4 0 -2 -4 0 16 50 which interval…

predicting key aspects using a table x -4 -3 -2 -1 0 1 2 3 4 f(x) -54 -20 -4 0 -2 -4 0 16 50 which interval contains a local maximum for this function? which interval contains a local minimum for this function?

predicting key aspects using a table x -4 -3 -2 -1 0 1 2 3 4 f(x) -54 -20 -4 0 -2 -4 0 16 50 which interval contains a local maximum for this function? which interval contains a local minimum for this function?

Answer

Explanation:

Step1: Recall local - max/min definition

A local maximum occurs when the function value is greater than the values at neighboring points, and a local minimum occurs when the function value is less than the values at neighboring points.

Step2: Analyze the function values

Looking at the table of (x) and (f(x)) values: When (x=-1), (f(-1) = 0). The values of (f(x)) for (x=-2) is (-4) and for (x = 0) is (-2). Since (0>-4) and (0 > - 2), there is a local maximum in the interval ((-2,0)). When (x = 1), (f(1)=-4). The values of (f(x)) for (x = 0) is (-2) and for (x=2) is (0). Since (-4<-2) and (-4 < 0), there is a local minimum in the interval ((0,2)).

Answer:

Local maximum interval: ((-2,0)) Local minimum interval: ((0,2))