AP Calculus

Special Focus: The Fundamental
Theorem of Calculus
12. g 0
( − 2)
= − 1, g 1
( − 2) = − 1.
5
Questions 13 and 14 foreshadow the Fundamental Theorem. The functions f 0 and f 1 are
antiderivatives of y = 1.5, while g 0
and g 1
are antiderivatives of y = 0.5. For each unit that
x increases, f0 ( x ) and f1 ( x ) increase by 1.5. For each unit that x increases, g0 ( x ) and
g1 ( x) increase by 0.5. In a later activity, students will see that a similar result applies to
any continuous integrand, not just constant ones.
13. The slope of each line is 1.5, the same as the integrand.
14. The slope of each line is 0.5, the same as the integrand.
24
AP® Calculus: 2006–2007 Workshop Materials