Mathematics

Problem

A smooth graph of

y=h(x)

is increasing on the interval

1<x<5

. Near

x=2

the tangent line appears to make a

30^\circ

angle with the horizontal, while near

x=4

the tangent line appears to make a

60^\circ

angle with the horizontal. Which of the following correctly compares

h'(2)

and

h'(4)

? a)

h'(2)>h'(4)

h'(2)=h'(4)

h'(2)<h'(4)

h'(2)<0<h'(4)