Question

Find the inflection point of the function of f(x) = x³ -6x² +12x

Answer 1

Points of inflections are zeroes of the second derivative. We have:

$f(x)=x^3-6x^2+12x\implies f'(x)=3x^2-12x\implies f''(x)=6x-12$

So, the second derivative equals zero if and only if

$f''(x)=0\iff 6x-12=0 \iff 6x=12 \iff x=2$

So, this is the only point of inflection of this function.