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Let f(x)=2x 3 −24x+2 Input the interval(s) on which f is increasing. Input the interval(s) on which f is decreasing. Find the intervals on which f is concave up. Find the intervals on which f is concave down. Using Interval Notation If an endpoint is included, then use [ or ]. If not, then use ( or ). For example, the interval from -3 to 7 that includes 7 but not -3 is expressed (-3,7]. For infinite intervals, use Inf for ∞ (infinity) and/or -Inf for -∞ (-Infinity). For example, the infinite interval containing all points greater than or equal to 6 is expressed [6,Inf). If the set includes more than one interval, they are joined using the union symbol U. For example, the set consisting of all points in (-3,7] together with all points in [-8,-5) is expressed [-8,-5)U(-3,7]. If the answer is the empty set, you can specify that by using braces with nothing inside: { } You can use R as a shorthand for all real numbers. So, it is equivalent to entering (-Inf, Inf). You can use set difference notation. So, for all real numbers except 3, you can use R-{3} or (-Inf, 3)U(3,Inf) (they are the same). Similarly, [1,10)-{3,4} is the same as [1,3)U(3,4)U(4,10). WeBWorK will not interpret [2,4]U[3,5] as equivalent to [2,5], unless a problem tells you otherwise. All sets should be expressed in their simplest interval notation form, with no overlapping intervals.

Solution:Critical points are: Using 1st derivative test:X<-2Let x=-3 Hence f(x) is increasing (-∞,-2]-2<X<2Let x=1 Hence f(x) is decreasing [-2,2]x>2Let x=3 Hence f(x) is…