WOLFRAM|DEMONSTRATIONS PROJECT

Napier's Inequality (I)

​
a
0.5
b
3.2
Napier's inequality: If
0<a<b
, then
1
b
<
lnb-lna
b-a
<
1
a
.
Observe that in the graphic,
lnb-lna
b-a
, the slope of the secant line passing through
(a,lna)
and
(b,lnb)
, is between the slopes of the tangent lines at
x=b
and
x=a
.