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Question Number 74265 by Maclaurin Stickker last updated on 21/Nov/19
Determinethevaluesofm∈Rforwhichthefunctionf(x)=12x2−mx+misthesetofrealnumbers.
Answered by MJS last updated on 21/Nov/19
2x2−mx+m=0x=m±m(m−8)4togetnozeros:m(m−8)<0⇒0<m<8for0<m<8:∀x∈R:2x2−mx+m>0inthiscasef(x)isdefinedforx∈Rbuttherangeis0<f(x)⩽228m−m2
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