AP Calculus AB / Differentiation: Definition and Basic Derivative Rules / Question No. 7

7. The graph of a function \( f \) is shown in the figure below. Which of the following statements must be false?

\( f(x) \) is defined for \( 0 \leq x \leq b \).

\( f(b) \) exists.

\( f'(b) \) exists.

\(\lim\limits_{{x \to a}} f'(x) \) exists.

Answer is: option3 - \( f'(b) \) exists.

Solution:

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Home Practice Questions AP Calculus AB Differentiation: Definition and Basic Derivative Rules Question No. 7