AP Calculus BC 6.4 Fundamental Theorem Overview

Review the Fundamental Theorem by moving between accumulation functions, antiderivatives and definite-integral evaluations.

Covered syllabus points

[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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