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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 $[1-8]$ and the maximum one is $[1-9]$ . 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: 2,585 Thanks: 1430 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. Thanks from topsquark June 15th, 2019, 11:22 AM #3 Senior Member   Joined: Feb 2016 From: Australia Posts: 1,839 Thanks: 653 Math Focus: Yet to find out. At your service m'lord https://www.desmos.com/calculator/kiq4ivf6u5 Thanks from topsquark June 15th, 2019, 11:42 AM   #4
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Quote:
 Originally Posted by Farzin 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 $[1-8]$ and the maximum one is $[1-9]$ . My answer is the maximum is $\dfrac 5 4$ and the minimum is $1$ but I think I am wrong
endpoint values ...

$f(0) = 1$, $f(2) = 1$

for $x \in (0,1)$, $f(x) = (1-x)+(2x-x^2) = 1 + x - x^2$

max on this interval is $f \left(-\dfrac{b}{2a} \right) = f(1/2) = 5/4$

for $x \in [1,2)$, $f(x) = (x-1)+(2x-x^2) = -1 + 3x - x^2$

$f(1) =1$, 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. Tags maximum or minimum Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Monox D. I-Fly Pre-Calculus 4 October 13th, 2014 05:58 AM Mathforfun21 Calculus 1 May 14th, 2013 02:12 AM bilano99 Calculus 7 March 19th, 2013 04:56 PM panky Algebra 1 November 6th, 2011 06:59 AM token22 Real Analysis 7 October 9th, 2011 01:50 PM

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