What are the critical values, if any, of $f (x) = | 3 x - 4 |$ $f(x)= abs(3x-4)$ ?

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What are the critical values, if any, of $f (x) = | 3 x - 4 |$ $f(x)= abs(3x-4)$ ?

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Answer 1 · 2017-12-21T16:45:56

The only critical value is $\frac{4}{3}$ $4/3$

Explanation:

$c$ $c$ is a critical value fo a function, $f$ $f$ if and only if $c i s \in t h e d o m a \in o f$ $c is in the domain of$ f $and$ $and$ f'(c) = 0 $or$ $or$ f'(c) does not exist.

For $f (x) = | 3 x - 4 |$ $f(x) = abs(3x-4)$ , the domain is $(- \infty, \infty)$ $(-oo,oo)$

$f'(x) = {(-3,x < 4/3),(3,x > 4/3):}$

$f'(x)$ is never $0$ ,

but $f'(4/3)$ does not exist. (The left and right limits of the difference quotient are unequal.)

So, the only critical value is $4/3$

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What are the critical values, if any, of $f (x) = | 3 x - 4 |$ $f(x)= abs(3x-4)$ ?

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What are the critical values, if any, of f(x)= abs(3x-4) f(x)=|3x−4|f(x)= abs(3x-4) ?

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What are the critical values, if any, of $f (x) = | 3 x - 4 |$ $f(x)= abs(3x-4)$ ?