Question

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

Answer 1

The only critical value is `4/3`

Explanation:

`c` is a critical value fo a function, `f` if and only if `c is in the domain of`f`and`f'(c) = 0`or`f'(c) does not exist.

For `f(x) = abs(3x-4)`, the domain is `(-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`