F(x) has a double root x=1, hence it is the turning point of the curve. It will touch the x axis at x=1 and then turn back, as can be seen from the graph

For ascertaining if any of the roots are inflection points, we find f”(x)

F(x)= x⁴+3x³-3x²-7x +6

F’(x)= 4x³ +9x² -6x-7

F “ (x) = 12x² +18x -6.

Since the roots are 1 ,1,-2 and -3, F “(x) ≠ 0 for any of x= 1, -2 and -3. Hence none of the roots are the inflection points.

As seen from the graph , there are two local minima and one local maxima.

****