The function f(x) = |x - 24| is | vedclass

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(D) $f(x) = |x - 24| = \begin{cases} -x + 24, & x < 24 \ x - 24, & x \geq 24 \end{cases}$ $\lim_{x ightarrow 24^{-}} f(x) = \lim_{x ightarrow 24}

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continuous on $[0, 25]$,but not differentiable on $[0, 25]$

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(D) $f(x) = |x - 24| = \begin{cases} -x + 24, & x $\lim_{x ightarrow 24^{-}} f(x) = \lim_{x ightarrow 24} (-x + 24) = 0$ $\lim_{x ightarrow 24^{+}} f(x) = \lim_{x ightarrow 24} (x - 24) = 0$ and $f(24) = 0$ Since the left-hand limit,right-hand limit,and the value of the function at $x = 24$ are equal,$f$ is continuous on $[0, 25]$. Now,check for differentiability at $x = 24$: Left-hand derivative: $\lim_{x ightarrow 24^{-}} \frac{f(x) - f(24)}{x - 24} = \lim_{x ightarrow 24} \frac{-x + 24 - 0}{x - 24} = -1$ Right-hand derivative: $\lim_{x ightarrow 24^{+}} \frac{f(x) - f(24)}{x - 24} = \lim_{x ightarrow 24} \frac{x - 24 - 0}{x - 24} = 1$ Since the left-hand derivative $
eq$ right-hand derivative,$f$ is not differentiable at $x = 24$. Therefore,$f$ is continuous on $[0, 25]$,but not differentiable on $[0, 25]$.

The function $f(x) = |x - 24|$ is

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