Mathematics

Problem

Let

f

be differentiable and strictly increasing on an interval containing

x=1

and

x=4

. Suppose

f(1)=3

with

f'(1)=0.5

and

f(4)=8

with

f'(4)=2.1

. Let

g=f^{-1}

. Calculate

g'(3)

and

g'(8)

, then indicate which of the two slopes has the greater magnitude.