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Question: If f(x) = a ln\|x\| + bx<sup>2</sup> + x has extremas at x = 1 and x = 3 then...

If f(x) = a ln|x| + bx2 + x has extremas at x = 1 and x = 3 then

A
B
C

a=−34,b=−18a = - \frac { 3 } { 4 } , b = - \frac { 1 } { 8 }

D

a=−34,b=18a = - \frac { 3 } { 4 } , b = \frac { 1 } { 8 }

Answer

a=−34,b=−18a = - \frac { 3 } { 4 } , b = - \frac { 1 } { 8 }

Explanation

Solution

f(x) = ax\frac { a } { x } + 2bx + 1.

Thus x = 1 and x = 3 are the roots of f(x) = 0 i.e. of 2bx2 + x + a = 0.

⇒ −12b=4,a2b=3- \frac { 1 } { 2 b } = 4 , \frac { a } { 2 b } = 3

⇒ b = −18- \frac { 1 } { 8 }, a = −34- \frac { 3 } { 4 }