`g(t) = |3t - 4|` Find the critical numbers of the function

Textbook Question

Chapter 4, 4.1 - Problem 34 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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sciencesolve | Teacher | (Level 3) Educator Emeritus

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The modulus of the equation of the function is defined as it follows:

`|3t - 4| = 3t - 4 if 3t - 4>=0 => t >= 4/3`

or

`|3t - 4| = 4 - 3t if t < 4/3`

You need to evaluate the critical numbers of the function, hence, you need to solveĀ  t the equation g'(t) = 0, in both cases.

For 't in [4/3,oo)' yields 'g'(t) = (3t - 4)' => g'(t) = 3`

Notice that `g'(t) != 0` for all values of `t in [4/3,oo).`

For `t in (-oo,4/3)` yields `g'(t) = (4 - 3t)' => g'(t) = -3`

Notice that `g'(t) != 0` for all values of `t in (-oo,4/3).`

Hence, there are no critical numbers for the given function such as `g'(t) = 0.`

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