Find the inflection point(s) of the function f(x)=ln(x2-4x+5)

Question

Find the inflection point(s) of the function f(x)=ln(x²-4x+5)

Answer 1

Graph the function! The polynomial in the problem has no real roots.

1st derivative: (2x-4)/(x²-4x+5)

Numerator of the 2nd derivative: -x² + 4x - 3; roots of the numerator:1 and 3.

Therefore, inflection points at x=1 and x=3...and this can be seen on the graph!