First of all, the inflection point can't be an extreme point, and the extreme point can't be an inflection point.

The nature of both is contradictory.

So c must be wrong.

Then we know that f(x)=|x( 1-x)|≥0 holds.

And f(0)=|0*( 1-0)|=0.

However, in the centripetal neighborhood of x=0, F (x) > 0 holds.

Therefore, f(x)≥f(0) holds in the centripetal neighborhood of x=0.

According to the definition of extreme point, x=0 is the minimum point of f(x).

So choose one