AP Calculus AB / limits and continuity / Question No. 48

48. Let \( f \) be a continuous function on the closed interval \([-2, 7]\). If \( f(-2) = 5 \) and \( f(7) = -3 \), then the Intermediate Value Theorem guarantees that

\( f'(c) = 0 \) for at least one \( c \) between \(-2\) and \(7\)

\( f'(c) = 0 \) for at least one \( c \) between \(-3\) and \(5\)

\( f(c) = 0 \) for at least one \( c \) between \(-3\) and \(5\)

\( f(c) = 0 \) for at least one \( c \) between \(-2\) and \(7\)

Answer is: option4

\( f(c) = 0 \) for at least one \( c \) between \(-2\) and \(7\)

Solution:

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