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June 15th, 2019, 10:46 AM  #1 
Newbie Joined: Mar 2017 From: Norway Posts: 26 Thanks: 0  Maximum/Minimum
Please help me with this question: If a function $f(x)$ in the domain $x ∈ [0, 2]$ is $f(x) = x − 1 + x^2 − 2x$, then the minimum value is $[18]$ and the maximum one is $[19]$ . My answer is the maximum is $\dfrac 5 4$ and the minimum is $1$ but I think I am wrong Last edited by Farzin; June 15th, 2019 at 11:23 AM. 
June 15th, 2019, 11:17 AM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,496 Thanks: 1371 
first thing I would do is hit an online graphic site and graph the thing. The minimum does indeed appear to be 1, and the maximum is $\dfrac 5 4$ as well. I can't say I understand how you came up with these correct answers given what you've written. 
June 15th, 2019, 11:22 AM  #3 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,830 Thanks: 648 Math Focus: Yet to find out.  
June 15th, 2019, 11:42 AM  #4  
Math Team Joined: Jul 2011 From: Texas Posts: 2,978 Thanks: 1573  Quote:
$f(0) = 1$, $f(2) = 1$ for $x \in (0,1)$, $f(x) = (1x)+(2xx^2) = 1 + x  x^2$ max on this interval is $f \left(\dfrac{b}{2a} \right) = f(1/2) = 5/4$ for $x \in [1,2)$, $f(x) = (x1)+(2xx^2) = 1 + 3x  x^2$ $f(1) =1$, and max on this interval is $f \left(\dfrac{b}{2a} \right) = f(3/2) = 5/4$  
June 15th, 2019, 11:58 AM  #5 
Newbie Joined: Mar 2017 From: Norway Posts: 26 Thanks: 0 
Thank you very much, that was a great help. Then I was right.


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