Let $f(x)$ be a piecewise function defined as $f(x) = \begin{cases} x^2 - 1 & ext{for } x \le 2 \ 3x - 3 & ext{for } x 2 \end{cases}$. Is $f$ differentiable at $x=2$?

Question

Let $f(x)$ be a piecewise function defined as $f(x) = \begin{cases} x^2 - 1 &	ext{for } x \le 2 \ 3x - 3 &	ext{for } x > 2 \end{cases}$. Is $f$ differentiable at $x=2$?

Accepted Answer

q2_c

Let $f(x)$ be a piecewise function defined as $f(x) = \begin{cases} x^2 - 1 &\text{for } x \le 2 \ 3x - 3 &\text{for } x > 2 \end{cases}$ . Is $f$ differentiable at $x=2$ ?

Explanation

Core Concept

Correct Answer

Let f(x)f(x)f(x) be a piecewise function defined as f(x)={x2−1for x≤2 3x−3for x>2f(x) = \begin{cases} x^2 - 1 &\text{for } x \le 2 \ 3x - 3 &\text{for } x > 2 \end{cases}f(x)={x2−1​for x≤2 3x−3​for x>2​. Is fff differentiable at x=2x=2x=2?

Explanation

Core Concept

Correct Answer

Let $f(x)$ be a piecewise function defined as $f(x) = \begin{cases} x^2 - 1 &\text{for } x \le 2 \ 3x - 3 &\text{for } x > 2 \end{cases}$ . Is $f$ differentiable at $x=2$ ?