1. on what intervals is ( f ) increasing?\nanswer (in interval notation):\n2. on what intervals is ( f )…

1. on what intervals is ( f ) increasing?\nanswer (in interval notation):\n2. on what intervals is ( f ) decreasing?\nanswer (in interval notation):\n3. at what values of ( x ) does ( f ) have a relative maximum?\nanswer (separate by commas): ( x=)\n4. at what values of ( x ) does ( f ) have a relative minimum?\nanswer (separate by commas): ( x=)

1. on what intervals is ( f ) increasing?\nanswer (in interval notation):\n2. on what intervals is ( f ) decreasing?\nanswer (in interval notation):\n3. at what values of ( x ) does ( f ) have a relative maximum?\nanswer (separate by commas): ( x=)\n4. at what values of ( x ) does ( f ) have a relative minimum?\nanswer (separate by commas): ( x=)

Answer

Explanation:

Step1: Determine increasing intervals

A function (y = f(x)) is increasing when the slope of the tangent line (or the visual trend of the graph) is positive. Looking at the graph, we can see that the function is increasing on the intervals ((-6,-4)) and ((-2,0)) and ((2,4)).

Step2: Determine decreasing intervals

A function (y = f(x)) is decreasing when the slope of the tangent line (or the visual trend of the graph) is negative. From the graph, the function is decreasing on the intervals ((-4,-2)) and ((0,2)) and ((4,6)).

Step3: Find relative maximum points

A relative maximum occurs at a point where the function changes from increasing to decreasing. From the graph, the (x -)values of relative maximum points are (x=-4,x = 0,x=4).

Step4: Find relative minimum points

A relative minimum occurs at a point where the function changes from decreasing to increasing. From the graph, the (x -)values of relative minimum points are (x=-2,x = 2,x=6).

Answer:

  1. ((-6,-4)\cup(-2,0)\cup(2,4))
  2. ((-4,-2)\cup(0,2)\cup(4,6))
  3. (x=-4,0,4)
  4. (x=-2,2,6)