A function has a sharp corner at x = 2. There it is

Continuous but not differentiable Corners ⇒ left/right derivatives differ → not differentiable. The function can still be continuous.

Continuous but not differentiable

Differentiable but not continuous

Connecting Differentiability and Continuity

AP Calculus AB· difficulty 2/5

x = 2

Explanation

Corners \Rightarrow left/right derivatives differ \to not differentiable. The function can still be continuous.

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