指數與對數(9)
Author: 藍邦偉　老師

(1) 指數函數圖形遞增⇔a>1

$ (2)設A(h-d,0),B(h,0),C(h+d,0) $

$ ⇒D(h-d,a^{h-d}),E(h,a^h),F(h+d,a^{h+d}) $

$ ⇒\overline{AD} +\overline{CF}=a^{h-d}+a^{h+d}$

$ =\frac{a^h}{d} +d×a^h=a^h(d+\frac{1}{d})$

$ >2×a^h=2×\overline{BE} $

(3) \overline{BE}-\overline{AD}=a^h-a^{h-d}=a^h(1-\frac{1}{a^d})

$ \overline{CF}-\overline{BE}=a^{h+d}-a^h =a^h(a^d-1)$

(4)\overline{AD}×\overline{CF}=a^{h-d}×a^{h+d}=a^{h-d+h+d}=a^{2h}=(a^h)^2

$ =\overline{BE}² $

(5)\overline{AD}×\overline{CF}=a^{-d}×a^{+d}=a^0=1

n = 0 (slider from 0 to 12, step 1)