# Napier's Inequality (I)

Napier's Inequality (I)

Napier's inequality: If , then <<.

0<a<b

1

b

lnb-lna

b-a

1

a

Observe that in the graphic, , the slope of the secant line passing through and , is between the slopes of the tangent lines at and .

lnb-lna

b-a

(a,lna)

(b,lnb)

x=b

x=a