Question

.设f(x)=ax³＋bx²＋cx＋d(a＞0),则f(x)为增函数的充要条件是

A.b²－4ac＞0                                                  B.b＞0,c＞0

C.b=0,c＞0                                                      D.b²－3ac＜0

Answer 1

D

解析:

本题考查导数与函数单调性的关系.

∵f′(x)=3ax²＋2bx＋c(a＞0),

要使f(x)在R上是增函数，只需f′(x)＞0,

即只需3ax²＋2bx＋c＞0恒成立.

∵a＞0,∴只需Δ=4b²－4×3ac＜0,即b²－3ac＜0.