How do you find the inflections points for #f(x) = (1/3)x^3-x^2-8x+2#?

1 Answer
Jul 22, 2015

The unique inflection point is #(x,y)=(1,-20/3)#.

Explanation:

The first derivative is #f'(x)=x^2-2x-8# and the second derivative is #f''(x)=2x-2#.

The second derivative changes sign (from negative to positive) at #x=1#, so this is the first coordinate of the unique inflection point of #f# (where, in this case, the graph of #y=f(x)# changes from concave down to concave up).

The second coordinate of the unique inflection point is #f(1)=1/3-1-8+2=-20/3#.

Therefore, the unique inflection point is #(x,y)=(1,-20/3)#.