Studying for physics test?

(b) You simply need to find where dU/dx = 0 (that is, where U is a minimum).

dU/dx = 0 = 4ε(-12σ^12/x^13 + 6σ^6/x^7) → divide by 4εσ^6
0 = -12σ^6/x^13 + 6/x^7
12σ^6/x^13 = 6/x^7 → multiply by x^13 / 6
2σ^6 = x^6
x = 0.263nm * 1.122 = 0.295 nm

c) If your plot looks like a "U", it's stable.
If it looks like a "∩" it's unstable.
Other shapes, you'll have to decide.

Hope this helps!