Let $f(x)= 10-6 x^2 + 2 x^3$

Input the interval(s) on which $f$ is increasing.

Input the interval(s) on which $f$ is decreasing.

Find the point(s) at which $f$ achieves a local maximum.

Find the point(s) at which $f$ achieves a local minimum.

Find the intervals on which $f$ is concave up.

Find the intervals on which $f$ is concave down.

Find all inflection points.