已知0 若三角形ABC的面积为S，求S=f(t)
解:y=logax是减函数,
分别从A(t,log,t),B(t+2,log,(t+2)),C(t+4,log,(t+4))向y轴作垂线交y轴于,
A1(0,log,t),B1(0,log,(t+2)),C1(0,log,(t+4))
梯形AA1C1C的面积:[t+(t+4)]×[log,t-log,(t+4)]/2=(t+2)×[log,t-log,(t+4)]
同理:梯形AA1B1B的面积:(t+1)×[log,t-log,(t+2)]
与梯形AA1B1B的面积:(t+3)×[log,(t+2)-log,(t+4)]
ΔABC的面积S=梯形AA1C1C的面积-(梯形AA1B1B的面积+梯形AA1B1B的面积)
=(t+2)×[log,t-log,(t+4)]-{(t+1)×[log,t-log,(t+2)]
+(t+3)×[log,(t+2)-log,(t+4)]}
=log,t+log,(t+4)-2log,(t+2)
=log,t(t+4)/(t+2)*(t+2)
S=log,t(t+4)/(t+2)*(t+2)
。
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