Q. If $f(x) = a\log_{e}{|x|} + bx^{2} + x$ 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) None of these
Explanation
(a)
For $x > 0$ or $x < 0$
$f^{'}(x) = \frac{a}{x} + 2bx + 1$
$\because\ \ f^{'}(1) = 0\ \ \ \Rightarrow \ \ \ a + 2b + 1 = 0$ …(i)
And $f^{'}(3) = 0\ \ \Rightarrow \ \ \frac{a}{3} + 6b + 1 = 0$ …(ii)
On solving Eqs. (i) and (ii), we get
$a = - 3/4,\ \ b = - 1/8$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.