Example 20 Continuity and Differentiability - Search Videos

Differentiability and continuity

Differentiability and continuity

We explore the notion of differentiability at a point and its relationship with continuity, using the definition of a derivative. If a function is differentiable at x = c, then it is continuous at x = c. However, a function being continuous does not guarantee that it is differentiable, as demonstrated with an absolute value function.

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Differentiability and continuity

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$TQ) Let 𝛼,𝛽∈ℝ be such that the function. 𝑓(𝑥)={(2𝛼(𝑥^2−2)+2𝛽𝑥&,𝑥1 (𝛼+3)𝑥+(𝛼−𝛽)&,𝑥≥1)$

TQ) Let 𝛼,𝛽∈ℝ be such that the function. 𝑓(𝑥)={(2𝛼(𝑥^2−2)+2𝛽𝑥&,𝑥1 (𝛼+3)𝑥+(𝛼−𝛽)&,𝑥≥1)

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