Question

已知a＞1,函數(shù)f(x)=求函數(shù)f(x)在x∈［1,2］時(shí)的最小值.

Answer 1

解:(1)當(dāng)1＜a≤2時(shí),

∵x∈［1,a］時(shí),f′(x)≤0,                                                                                    ?

x∈(a,2］時(shí),f′(x)＞0,                                                                                        ?

∴f(x)_Min=f(a)=0.                                                                                                     ?

(2)當(dāng)a＞2時(shí),∵x∈［1,2］,?

∴x＜a.∴f(x)=x²·E^-ax,f′(x)=(2x-ax²)·E^-ax＜0.                                                        ?

∴f(x)在x∈［1,2］時(shí)是減函數(shù).                                                                       ?

∴f(x)_Min=f(2)=4E^-2a.