stuck on point of inflection problem

Question

Find the x-coordinate of the point of inflection of the function f(x)=x^3-x^2-x+1

Answer 1

The point of inflection is where the function changes from concave up to concave down or vice versa.  You can find this through the second derivative.

 

f'(x) = 3x^2-2x-1

f"(x)=6x-2

 

The function changes concavity where the second derivative is 0

 

0=6x-2  add 2 to both sides

2=6x  divide by 6

 

x=1/3