Let us consider the function

f(x)=x⁴18x²+31

a) This function has three critical points(x,y). Identify all of them. Just typex

yvalues, do not use parentheses. Order them so thatx is in ascending order. For example, if there are two points (-2,5) and (3,-2), then (-2,5) goes first and then (3,-2).

1. ( , )
2. ( , )
3. ( , )

b) Detemine regions where the function is increasing or decreasing. For type -100, for+type 100.

fis increasing on( , ) ( , )

fis decreasing on( , ) ( , )

c) Determine if the critical points from step a) (use the same order) are relative maxima/minima or not. TypeMaxif point is the relative maximum;Minif point is the relative minimum;Noif point is not relative extremum.

1.

2.

3.