Question

Find the critical number of the function.
g(t) = | 3t - 5 |
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Answer 1

\[
3t - 5 = 0, \text{when }~t = \frac 53\\
\text{For }~~t \gt \frac 53, ~~g(t) = 3t - 5;~~~~~g'(t) = 3 \\
\text{For }~~t \lt \frac 53, ~~g(t) = -3t + 5;~~g'(t) = -3 \\
\text{At }~~t = \frac 53, ~~g'\left (\frac 53^+\right ) = 3; ~~
g'\left (\frac 53^-\right ) = -3 \\
\text{Therefore, the derivative does not exist at }t = \frac 53. \\
t = \frac 53\text{ is a critical point.}
\]