Question

Find the points of inflection for the curves;
y = 5 - 2x - 3x² - x³

Answer 1

what's inflection?? :P

Answer 2

It's like the changes in curve and the sense of concavity.. :)

Answer 3

ohhhhhhh. so you mean the points where the direction changes. i feel stupid now that i don't know what this is :P

Answer 4

(-1,5)

Answer 5

y'=0-2-6x-3x^2
y''=0-0-6-6x=-6-6x
set y''=0 and solve for x
-6-6x=0
x=-1
if x=-1 then y=5-2(-1)-3(-1)^2-(-1)^3=5+2-3+1=5
does the inflection change at (-1,5)

well lets test the concavity before and after x=-1
choose a number before -1 such as 0; f''(0)=-6
choose a number after -1 such as 2; f''(2)=-6-6(2)=-6-12=-18
both are negative
that means the concavity did not change
that means there are no inflection points

Answer 6

f' gives slope
f'' gives concavity

f' = 0 gives min max
f'' = 0 gives inflection

Answer 7

i mean 0 isn't before -1

Answer 8

lol

Answer 9

which is it? ahhhhh!!!!!

Answer 10

choose a number before -1 such as -2; f''(-2)=-6-6(-2)=6
concavity changes=> inflection point at (-1,5)

Answer 11

i'm gonna go write my 1,2,3,'s now
later

Answer 12

I get it.. (±2, 5) thanks!

Answer 13

..... no

Answer 14

a cubic only has one inflection

Answer 15

y'=0-2-6x-3x^2
y''=0-0-6-6x=-6-6x

Answer 16

Oh alright..

Answer 17

art is really improving. like in the renaissance

Answer 18

lol

Answer 19

amsitre got it

Answer 20

now i am out before i get stuck