identify the coordinates of any local and absolute extreme points and inflection points. Graph the function.

Question

y = (x² - 1)²

Answer 1

y=(x^2-1)^2 = x^4 -2x^2 +1

y' = 4x^3 -4x= 0

4x(x^2-1)=0

4x(x+1)(x-1) = 0

local max and mins =

critical points are where x=-1,0 and 1, (-1,0), (0.1) and (1,0)

at x= -1 is local min

at x=0 is a local max

at x=1 is a local min

there is no global max

global min is y=0, a tie between (-1,0) and (1,0)

y" =12x^2 -4=0

x^2= 4/12 =1/3

x = 1/sqr3, -1/sqr3 = inflection points

it's sort of a "W" shaped curve

where end behavior has y approaching infinity