F(x) = x4 - 50x2 + 4
find the intervals on which f is increasing and decreasing. local min and max values. inflection points. intervals on which f is concave up and concave down.

So the question, based on the given function in your question, is asking to calculate on which value of F is increasing and decreasing  and base on my own research and calculation, I would say that the answer would be (5, -621). 
(-inf,0) concave up (0,inf) concave up, -5,5) concave down, decreasing (-inf,-5),  increasing (-5,0),  decreasing (0,5),  increasing (5,inf) and f(5) = (5)^4 - 50(5)^2 + 4 = (5,-621) MIN. I hope this would help 

x^3−x^2−12x=0

x(x^2-x-12)=0

x(x^2-4x+3x-12)=0

x(x(x-4)+3(x-4))=0

x(x+3)(x-4)=0

So the "zeros" are:

x=(-3,0,4)