Question

y=f(x)的定義域為［a,b］,設對任意x₁、x₂∈［a,b］且x₁≠x₂,記Δ=,則下列結論中正確的是

①y=f(x)在［a,b］上單調遞增的充要條件是Δ>0;②y=f(x)在［a,b］上單調遞減的充要條件是Δ<0;③y=

f(x)在［a,b］上是單調函數的充要條件是Δ≠0.

A.①②                                                                   B.②③

C.①③                                                                   D.①②③

Answer 1

解析:③不正確,因當Δ≠0時,若Δ>0,有x₁<x₂f(x₁)<f(x₂),若Δ<0,有x₁<x₂?f(x₁)>f(x₂),故當Δ≠0時,函數不單調.

答案:A