Question

I need someone to help me (in very simple terms ;)) how to: Graph each polynomial function. Factor first if the expression is not in factored form..
f(x)=x^2(x+1)(x-1)

Answer 1

to graph polynomial function , firstly i will find the point which intersect x-axis. the point that intersect x-axis has y=0
to find that, 0=x^2 (x+1)(x-1)
the values of x which fulfill the equation are x=0, x=-1, x=1

secondy, find the extreme point. use the derivative of the function
\[f \prime x =4x ^{3}-2x ^{}=0\]
so x=-1/2 and 1/2
then plug those value of x to the function to get the extreme value of y
you'll get y = 1/16

so you'll have some points :
(0,0) , (-1,0) , (1,0) (-1/2, 1/16), (1/2, 1/16)

finally just connect that points so now you have the graph

Answer 2

sorry, the value of y extreme is not 1/16 . it's -1/16

Answer 3

so the extreme points is (-1/2, -1/16) and (1/2, -1/16)

Answer 4

here, i attach the graph of the function

Answer 5

Thank you so much!!!!!!!!!! Great, great explanation!

Answer 6

you're welcome :)