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Find the minimum value of given expressionWhat is the answer of given question

parveen , 6 Years ago
Grade 12
anser 1 Answers
kkbisht

Last Activity: 6 Years ago

 
Let  y=x2+ 1/(x2-1)  +5 
To find minimum value of y we differentiate y w.r.t x we obtain
dy/dx = 2x + -1.2x/(x2-1)2 .For minima or maxima of y  dy/dx=0 => 2x =2x/(x2-1)2 =>x{(x2-1)2 -1}=0 
=>x=0 or x2-1=+-1=> x=0, x2=2 => x=0 , x=+-\sqrt{}2  Put x=0 , x=\sqrt{}2, x=-\sqrt{}successively we obtain
for x=0
y=0 +1/(0-1) +5 = 4
 
for x=\sqrt{}2
y= 2+ 1/(2-1) +5 = 8
 for x=-\sqrt{}2
y=2+1/(2-1) +5 =8
 So the minimum vale of the expression x2 + 1/(x2-1) +5 is 4  at x=0
 
 

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