CB.Calc.FUN-2.A: Explain the relationship between differentiability and continuity.

Explain the relationship between differentiability and continuity.

Example Problems

Is the function given below continuous and/or differentiable at

x = 3

?

w(x) = \begin{cases} (x - 3)^2 + 4 & \text{if } x \leq 3 \\ 4 & \text{if } x > 3 \end{cases}

Is the function given below continuous and/or differentiable at

x = 0

?

q(x) = \begin{cases} -4x & \text{if } x < 0 \\ 4x & \text{if } x \geq 0 \end{cases}

Is the function given below continuous and/or differentiable at

x = 1

?

u(x) = \begin{cases} x^3 & \text{if } x \leq 1 \\ 3x - 2 & \text{if } x > 1 \end{cases}

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