x -4 -3 -2 -1 0 1 2 3 4\nf(x) -54 -20 -4 0 -2 -4 0 16 50\nwhich interval contains a local maximum for this…

x -4 -3 -2 -1 0 1 2 3 4\nf(x) -54 -20 -4 0 -2 -4 0 16 50\nwhich interval contains a local maximum for this function?\nwhich interval contains a local minimum for this function?

x -4 -3 -2 -1 0 1 2 3 4\nf(x) -54 -20 -4 0 -2 -4 0 16 50\nwhich interval contains a local maximum for this function?\nwhich interval contains a local minimum for this function?

Answer

Explanation:

Step1: Recall local - extrema 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 values of (y = f(x)): When (x=-1), (f(-1) = 0), (f(-2)=-4) and (f(0)= - 2). Since (f(-1)>f(-2)) and (f(-1)>f(0)), there is a local maximum in the interval ((-2,0)). When (x = 2), (f(2)=0), (f(1)=-4) and (f(3)=16). Since (f(2)<f(1)) and (f(2)<f(3)), there is a local minimum in the interval ((1,3)).

Answer:

Local maximum interval: ((-2,0)) Local minimum interval: ((1,3))