mathmath333
  • mathmath333
find the minimum and maximum value of \(y\) if
Mathematics
chestercat
  • chestercat
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mathmath333
  • mathmath333
\(\large \color{black}{\begin{align} y=\text{max}(2x+3,x-1),\ -10\leq x\leq 10\hspace{.33em}\\~\\ \end{align}}\)
anonymous
  • anonymous
Since it is a linear function you can test the endpoints.
Michele_Laino
  • Michele_Laino
how is defined: \[\Large \max \left( {f\left( x \right),g\left( x \right)} \right)\]?

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Michele_Laino
  • Michele_Laino
is it a metric?
Michele_Laino
  • Michele_Laino
sorry, I remember now!
Michele_Laino
  • Michele_Laino
we can write this: \[\max \left( {f\left( x \right),g\left( x \right)} \right) = \frac{1}{2}\left\{ {f\left( x \right) + g\left( x \right) + \left| {f\left( x \right) - g\left( x \right)} \right|} \right\}\]
Loser66
  • Loser66
I am with @jayzdd
mathmath333
  • mathmath333
well answer given is \(\large \color{black}{\begin{align} & y_{\text{max}} =23\hspace{.33em}\\~\\ & y_{\text{min}} =-11\hspace{.33em}\\~\\ \end{align}}\)
anonymous
  • anonymous
I used a wrong formula
anonymous
  • anonymous
It must be\[y=\frac{3x+2+|x+4|}{2}\]
mathmath333
  • mathmath333
@Michele_Laino 's formula looks correct.
anonymous
  • anonymous
yeah, that's the correct formula
mathmath333
  • mathmath333
just for the record https://www.desmos.com/calculator/a9klmgww5t
mathmath333
  • mathmath333
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anonymous
  • anonymous
so we just need to plug three values for finding max and min, -10, -4 and 10
mathmath333
  • mathmath333
yes -10 and 10

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