Question

If $f\left(x\right)=alo{g}_e|x|+b{x}^2+x$ has extremum at x = 1 and x = 3, then

• A. a = -3/4, b= -1/8
• B. a=3/4, b= -1/8
• C. a =-3/4, b=1/8
• D. a=3,b=-4

Answer 1

The correct option is A

a = -3/4, b= -1/8

For $x>0orx<0f^{\prime }\left(x\right)=\frac{a}{x}+2bx+1\because f^{\prime }\left(1\right)=0\Rightarrow a+2b+1=0and{f}^{\prime }\left(3\right)=0\Rightarrow \frac{a}{3}+6b+1=0$
Solving Eqs. (i) and (ii), we get
a = - 3/4, b = -1/8