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y-x-2-2x-3x-2-find-the-largest-values-of-the-function-




Question Number 12697 by @ANTARES_VY last updated on 29/Apr/17
y=∣x−2∣+2x−3x^2   find  the  largest  values  of  the  function.
y=∣x2+2x3x2findthelargestvaluesofthefunction.
Answered by mrW1 last updated on 29/Apr/17
if x≥2:  y=x−2+2x−3x^2 =−3(x^2 −x+(1/4))−2+(3/4)=−3(x−(1/2))^2 −(5/4)  y_(max) =−(5/4) at x=(1/2)≱2 !    if x<2:  y=−x+2+2x−3x^2 =−3(x^2 −(1/3)x+(1/(36)))+2+(1/(12))=−3(x−(1/6))^2 +((25)/(12))  y_(max) =((25)/(12)) at x=(1/6)<2 ok!    max. value of function =((25)/(12)) at x=(1/6)
ifx2:y=x2+2x3x2=3(x2x+14)2+34=3(x12)254ymax=54atx=122!ifx<2:y=x+2+2x3x2=3(x213x+136)+2+112=3(x16)2+2512ymax=2512atx=16<2ok!max.valueoffunction=2512atx=16

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