SOLUTION: What is the minimum value of {{{f(x)=2x+abs(3x-1)}}}?

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Question 1020442: What is the minimum value of f%28x%29=2x%2Babs%283x-1%29?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
When x%3E=1%2F3,
abs%283x-1%29=3x-1
So then,
f%28x%29=2x%2B3x-1=5x-1
.
.
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When x%3C1%2F3,
abs%283x-1%29=-%283x-1%29=1-3x
So then,
f%28x%29=2x%2B1-3x=1-x
.
.
.
So the critical point is x=1%2F3, where the slope of the line goes from negative to positive.
So the function must be a minimum at that point.
f%281%2F3%29=5%281%2F3%29-1=5%2F3-1=2%2F3