AP Calculus AB 6.4 The Fundamental Theorem of Calculus and Accumulation Functions Questions

Practice AP Calculus Unit 6.4 questions on representing accumulation functions with definite integrals and differentiating those functions.

Covered syllabus points

FUN-5.A—Represent accumulation functions using definite integrals

[Maximum number: 2]

The continuous function f is defined on the closed interval $-6 \leq x \leq 12$ . The graph of f, consisting of two semicircles and one line segment, is shown in the figure.

$Graph of $f$$

Graph of $f$

Let g be the function defined by $g(x)=\int_{6}^{x} f(t) d t$ .

Find $g^{\prime}(8)$ . Give a reason for your answer.


$g^{\prime}(x)=f(x)$	Considers $g^{\prime}(x)=f(x)$	Point 1 (P1)
$g^{\prime}(8)=f(8)=1$	Answer	Point 2 (P2)
Scoring Notes for Part A
- A response that does not earn P1 can earn P2 with an implied application of the Fundamental Theorem of Calculus (e.g., $g^{\prime}(8)=1$ or f(8)=1 ).

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Covered syllabus points

Question 1