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EXAMINATION QUESTIONS 1. Find the maximum and minimum value of the function y = 2r8 - 15x2 + 36x + 11.(Durg, 2019) Ans.-6,39] |
| Answer» TION:ANSWERf(X)=2x 3 −15x 2 +36x+10→(i)differentiatew.rtox⇒f ′ (x)=6X 2 −30x+36⇒f ′ (x)=0⇒6x 2 −30x+36=0⇒x 2 −5x+6=0⇒x 2 −3x−2x+6=0⇒x(x−3)−2(x−3)=0⇒x=3,x=2againdifferentiatew.rtoxf ′ (x)=12x−30→(ii)Putx=2⇒f ′ (2)=24−30=−60,x=2pointmaximumandminimumvalueisf(2)=2×2 3 −15×2 2 +36×2+10⇒f(2)=16−60+71+10=38andputx=3ineq n (ii)⇒f ′ (3)=36−30=6Itispointmaximumandminimumvalueisf(3)=2×27−15×9+36×3+10=37 | |