Sketching a curve (1 Viewer)

[Monsterman]

How would I sketch x^3-2x^2+2x+5? like show how to find the stationary points?
Cause i differentiated it and completed the square and got 3((x-2/3)^2+10/9).. could someone confirm this cause i reckon i did it wrong..

 

[nonsenseTM]

I got y'=3((x-2/3)^2)+2/3 which is always greater than 0 , so always increases

and point of non horizontal inflex. at 2/3,155/27, as x appoaches +/- infinity, y appoaches +/- infinity

 

[adomad]

How would I sketch x^3-2x^2+2x+5?

y=x^3-2x^2+2x+5 - Wolfram|Alpha

 

[Monsterman]

^
thats useless when you want to know how to do it for an exam........

I got y'=3((x-2/3)^2)+2/3 which is always greater than 0 , so always increases

and point of non horizontal inflex. at 2/3,155/27, as x appoaches +/- infinity, y appoaches +/- infinity

how do you know the position of the inflexion point? because if you let the derivative equal zero you get a negative 2/9 and a squareroot.. which equals gayness

 

[cutemouse]

Solve y'=0 for stat pts. Determine their nature (using y' or y'' sign test).

Solve y''=0 and check for concavity changes for inflexions.