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AP Calculus AB/Unit 1: Limits and Continuity
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Continuity and Differentiability of a Piecewise Function

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Let gg be the function defined by g(x)={x2if x23x2if x>2g(x) = \begin{cases} x^2 & \text{if } x \leq 2 \\ 3x - 2 & \text{if } x > 2 \end{cases}. Which of the following statements about gg is true?

A

gg is differentiable but not continuous at x=2x = 2.

B

gg is continuous and differentiable at x=2x = 2.

C

gg is defined but neither continuous nor differentiable at x=2x = 2.

D

gg is continuous but not differentiable at x=2x = 2.

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