AP Calculus AB 2.4 Connecting Differentiability and Continuity Determining When Derivatives Do and Do Not Exist Questions

Practise AP Calculus AB 2.4 questions by connecting continuity with derivative existence in graphs and piecewise formulas.

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If $f(x)=\left\{\begin{array}{ll}x^{2} & \text { for } x \leq 1 \\ 2 x-1 & \text { for } x>1\end{array}\right.$ , then

f(x) is not continuous at x=1

f(x) is continuous at x=1 but $f^{\prime}(1)$ does not exist

$f^{\prime}(1)=2$

$\lim _{x \rightarrow 1} f(x)$ does not exist

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