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

1 Answer
Dec 21, 2017

Answer:

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#