All Questions Topic List
Algebra Questions
Previous in All Question Next in All Question
Previous in Algebra Next in Algebra
Question Number 151475 by mathdanisur last updated on 21/Aug/21
ifx∈Rprovethat:x6−x+1>0
Answered by dumitrel last updated on 21/Aug/21
I.ifx⩽0⇏−x⩾0;x6+1>0⇒x6−x+1>0II.ifx>0⇒x6+1=x6+15+15+15+15+15⩾am−gm⩾6x556>6x5>x⇒x6−x+1>0
Commented by mathdanisur last updated on 21/Aug/21
NiceSer,ThankYou
Answered by MJS_new last updated on 21/Aug/21
f(x)=x6−x+1f′(x)=6x5−1f″(x)=30x4f′(x)=0⇒x=161/5;f(161/5)≈.4>0f″(x)>0∀x∈R⇒⇒absoluteminimum>0
Terms of Service
Privacy Policy
Contact: info@tinkutara.com