List the location of all inflection points for the function $$f(x)=x^3-3x^2-4x+12$$

Question

stamp · Answer

aint an inflection point where the f''(x) = 0? So you solve the zeroes of f''(x) and then check the sign changes of f'(x) at those points

mathstudent55 · Answer

Correct.

loser66 · Answer

all elites here, you are safe hihihihi

ganeshie8 · Answer

you're right, but why do u bother checking for sign changes ?

stamp · Answer

fortunately f'(x) and f''(x) easy to find$$f'(x)=3x^2-6x-4$$$$f''(x)=6x-6$$

stamp · Answer

@ganeshie8 cus if it goes from + to + its not inflecting

mathstudent55 · Answer

All you need to do is find f", set it equal to zero, and find the zeroes.

stamp · Answer

$$f''(x)=6x-6$$$$f''(x)=0, x=1$$

stamp · Answer

So is x=1 an inflection point or is there other things to consider before making that claim

ganeshie8 · Answer

interesting, if psble could u explain quick how we can get + to + change on f'(x) ?

ganeshie8 · Answer

since its a cubic, only one inflection will be there. and it exists at x = 1 (from ur work)

stamp · Answer

$$f''(<1) =-$$$$f''(>1)=+$$

So I am supposed to look at the sign changes of f''(x) to the left and right of the zeros to f''(x)

stamp · Answer

I have my own resources to answer that question on my own, good to know x=1 is the inflection point. Thanks ya'll, moving on

ganeshie8 · Answer

Gotcha !! you do need to make sure sign change yes ! thank you too  :)