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2x21
1ҽx1ʱȺų x211xxxa1.ʵaȡֵΧΪ[1)
12֪f(x)eaxa(aRa0)
(1)f(x)x0ȡüֵʵaֵʱf(x)[2,1]ϵֵ (2)f(x)㣬ʵaȡֵΧ ⣺(1)f(x)ĶΪRf(x)ea
xxf(0)e0a0a1f(x)ex1
(ޣ0)f(x)<0f(x)ݼ(0)f(x)>0f(x) x0ʱf(x)ȡСֵa1Ҫ ֪f(x)[2,0)ϵݼ(0,1]ϵ 1
f(2)23f(1)ef(2)>f(1)
e1
f(x)[2,1]ֵΪ23.
e(2)f(x)eae>0.
ٵa>0ʱf(x)>0f(x) ҵx>1ʱf(x)ea(x1)>0. 1
x<0ʱȡx
xxxa?1??1?f??<1a?1?a<0
?a?
?a?
ຯf(x)㣬⣮
ڵa<0ʱf(x)ea0xln(a) (ޣln(a))f(x)<0f(x)ݼ (ln(a))f(x)>0f(x) xln(a)ʱf(x)ȡСֵ
f(x)㣬ȼf(ln(a))ee ʵaȡֵΧ(e0) 2, 2 ln(a) xaln(a)a2aaln(a)>0 - 5 -