Can you please check my answers and fix the ones if any that are wrong. Along with help on part d

Consider the following fun f(x)=(3/4)x^3- x^3-3x^2+6x
A.find relative extrema and identify max and min.
I got x=1 max ,±√2 min
B.determine the interval(s) where f(x) is decreasing and increasing
I got decreasing -√2>x, 1<x<√2
and increase -√2<x<1, x<√2
C.show that there are exactly two points of inflection. (Do not need to find points)
Cause y"=9x^2-6x+6
D. Show f(x) is concave up at x=2,x=-1 and x=2. Show that f(x) is concave down at x=0
I need help with this one

A and B are ok. As for C, just showing that f" is a quadratic does not mean that it has two roots.

However, if you went ahead and found that it must have two roots because the discriminant is positive, then ok.

f is concave up (down) if f" is positive (negative), so
f"(2) = 30 > 0, so f is concave up
similarly for the others.