MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties
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∘ angle with the horizontal, while near x=4 the tangent line appears to make a 60∘ angle with the horizontal. Which of the following correctly compares h′(2) and h′(4)?
(a) h′(2)>h′(4)
(b) h′(2)=h′(4)
(c) h′(2)<h′(4)
(d) h′(2)<0<h′(4)