ap-calculus-ab None Q35

ap-calculus-ab · USA · -bc_1969-1998_multiple-choice-collection Indefinite & Definite Integrals Accumulation Function Analysis
35. If $F$ and $f$ are differentiable functions such that $F ( x ) = \int _ { 0 } ^ { x } f ( t ) d t$, and if $F ( a ) = - 2$ and $F ( b ) = - 2$ where $a < b$, which of the following must be true?
(A) $\quad f ( x ) = 0$ for some $x$ such that $a < x < b$.
(B) $\quad f ( x ) > 0$ for all $x$ such that $a < x < b$.
(C) $f ( x ) < 0$ for all $x$ such that $a < x < b$.
(D) $\quad F ( x ) \leq 0$ for all $x$ such that $a < x < b$.
(E) $\quad F ( x ) = 0$ for some $x$ such that $a < x < b$.
35. If $F$ and $f$ are differentiable functions such that $F ( x ) = \int _ { 0 } ^ { x } f ( t ) d t$, and if $F ( a ) = - 2$ and $F ( b ) = - 2$ where $a < b$, which of the following must be true?\\
(A) $\quad f ( x ) = 0$ for some $x$ such that $a < x < b$.\\
(B) $\quad f ( x ) > 0$ for all $x$ such that $a < x < b$.\\
(C) $f ( x ) < 0$ for all $x$ such that $a < x < b$.\\
(D) $\quad F ( x ) \leq 0$ for all $x$ such that $a < x < b$.\\
(E) $\quad F ( x ) = 0$ for some $x$ such that $a < x < b$.\\