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

.