Q.Let a,belement ofR be such that the function f given by f left parenthesis x right parenthesis equals log open parentheses x close parentheses plus b x squared plus a x xnot equal to0 has extreme values at x=-1,2
STATEMENT 1:f has local maximum at x=-1 and at x=2
STATEMENT 2:a=0.5 b=-0.25
then
1:S1 is false S2 is true
2:S1 is true S2 is true, correct explanation
3:S1 is true S2 is true,not a correct explanation
4:S1 is true S2 is false 

Asked by Ravi consul | 22nd Mar, 2015, 12:17: AM

Expert Answer:

G i v e n space t h a t space f open parentheses x close parentheses equals log open parentheses x close parentheses plus b x squared plus a x comma space x not equal to 0 f apostrophe open parentheses x close parentheses equals 1 over x plus 2 b x plus a S i n c e space f open parentheses x close parentheses space h a s space e x t r e m e space v a l u e s space a t space x equals negative 1 space a n d space a t space x equals 2 comma space w e space h a v e comma f apostrophe open parentheses negative 1 close parentheses equals 0 space a n d space f apostrophe open parentheses 2 close parentheses equals 0 rightwards double arrow fraction numerator 1 over denominator open parentheses negative 1 close parentheses end fraction plus 2 b open parentheses negative 1 close parentheses plus a equals 0 space a n d space fraction numerator 1 over denominator open parentheses 2 close parentheses end fraction plus 2 b open parentheses 2 close parentheses plus a equals 0 rightwards double arrow negative 1 minus 2 b plus a equals 0 space a n d space 1 plus 8 b plus 2 a equals 0 rightwards double arrow a equals 1 half space a n d space b equals fraction numerator negative 1 over denominator 4 end fraction rightwards double arrow a equals 0.5 space a n d space b equals negative 0.25 S u b s t i t u t i n g space t h e space v a l u e s space a equals 0.5 space a n d space b equals negative 0.25 f open parentheses x close parentheses equals log open parentheses x close parentheses minus 0.25 x squared plus 0.5 x f open parentheses negative 1 close parentheses equals log open parentheses negative 1 close parentheses minus 0.25 open parentheses negative 1 close parentheses squared plus 0.5 open parentheses negative 1 close parentheses equals u n d e f i n e d f open parentheses 2 close parentheses equals log open parentheses 2 close parentheses minus 0.25 open parentheses 2 close parentheses squared plus 0.5 open parentheses 2 close parentheses T h u s comma space s t a t e m e n t space 1 space i s space f a l s e space a n d space s t a t e m e n t space 2 space i s space t r u e. H e n c e space o p t i o n space 1 space i s space t h e space c o r r e c t space o p t i o n.

Answered by Vimala Ramamurthy | 23rd Mar, 2015, 12:53: PM

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