How can I find the points of inflexion on a curve and determine whether they are horizontal points of inflexion? For example on this curve: y=x^3(x-1)

Question

kc_kennylau · Answer

Have you learnt differentiation? Just asking :)

tracy23 · Answer

Lol :D yes I have

kc_kennylau · Answer

What's the slope of the tangent of the curve at horizontal points?

tracy23 · Answer

What do you mean by 'at horizontal points'?

kc_kennylau · Answer

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tracy23 · Answer

Isn't the slope there 0?

kc_kennylau · Answer

exactly :D

kc_kennylau · Answer

So if it's a horizontal point, f'(x) will be 0 :)

tracy23 · Answer

Right! :D

tracy23 · Answer

So can you help me out in finding the points of inflection on this curve? ^_^
y=x^3(x-1)

kc_kennylau · Answer

The inflection points are the points whose second derivative is 0, i.e. f''(x)=0 :)

kc_kennylau · Answer

actually what did you mean by horizontal points?

tracy23 · Answer

Okay- so in a horizontal point of inflection f'(x) and f"(x) would both be equal to zero right?

kc_kennylau · Answer

can you tell me what's a horizontal point of inflection lol, like draw a graph

tracy23 · Answer

Lol xD I would if I knew what it was :P That's exactly the part I get confused about... I can find the points of inflection but I can't tell which is a horizontal one :/ Its this question in my book... it says: Find the coordinates of any points of inflection on the curve y=x^3(x-1) and determine whether they are horizontal points of inflection.

kc_kennylau · Answer

Think so :)

kc_kennylau · Answer

So if f'(x)=0 and f''(x)=0 it's a horizontal point of inflection :)

tracy23 · Answer

Alrighty! XD Thanks a lot! :D You really helped :) It was my first time posting my question in here... glad you were there to help! (^.^)

kc_kennylau · Answer

thanks :) Your question made me research about points of inflection and you've taught me something new :D

tracy23 · Answer

haha lol :D great! Btw, what's your name?

tracy23 · Answer

Oh wow! Thanks for the medal! :D

kc_kennylau · Answer

My name is Kenny Lau K. C.:)

kc_kennylau · Answer

Lau is my surname, K.C. is my given name, Kenny is my English name

kc_kennylau · Answer

K.C. stands for Kin Chung

tracy23 · Answer

Nice to meet you Kenny! :) My name's Tracy :D Thanks again Kenny! :)

kc_kennylau · Answer

no problem :)