Question of the Day

25. If \( f \) is a differentiable function such that \( f(2) = 5 \) and \( f'(2) = 7 \), which of the following statements could be false?

\( \lim\limits_{x \to 2^-} f(x) = \lim_{x \to 2^+} f(x) \)

\( \lim\limits_{x \to 2} \frac{f(x) - 5}{x - 2} = 7 \)

\( \lim\limits_{h \to 0} \frac{f(2+h) - 5}{h} = 7 \)

\( \lim\limits_{h \to 0} f'(x) = 7 \)

Answer is: option4

\( \lim\limits_{h \to 0} f'(x) = 7 \)

Solution: