For a real constant aaa, consider
f(x)=x4−ax2+3xf(x) = x^4 - ax^2 + 3xf(x)=x4−ax2+3x
For exactly which values of aaa is fff convex on the whole real line?
Select all that apply.
a≤0a \le 0a≤0
a<0a < 0a<0 strictly — a=0a = 0a=0 has to be excluded, since there f′′(0)=0f''(0) = 0f′′(0)=0 rather than positive.
a≥0a \ge 0a≥0
Every real aaa: the x4x^4x4 term dominates, so the function is bowl-shaped either way.