FunctionHard
Question
The mapping f : R → R given by f(x) = x3 + ax2 + bx + c is a bijection if
Options
A.b2 ≤ 3a
B.a2 ≤ 3b
C.a2 ≥ 3b
D.b2 ≥ 3a
Solution
f : R → R, f(x) = x3 + ax2 + bx + c
f′(x) = 3x2 + 2ax + b
D ≤ 0 or 4a2 - 12b ≤ 0
or a2 ≤ 3b
f′(x) = 3x2 + 2ax + b
D ≤ 0 or 4a2 - 12b ≤ 0
or a2 ≤ 3b
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