Application Of Derivatives Question 7
Question 7 - 30 January - Shift 2
If the functions $f(x)=\frac{x^3}{3}+2 b x+\frac{ax^2}{2}$ and $g(x)=\frac{x^{3}}{3}+a x+b x^{2}, a \neq 2 b$ have a common extreme point, then $a+2 b+7$ is equal to
(1) 4
(2) $\frac{3}{2}$
(3) 3
(4) 6
Show Answer
Answer: (4)
Solution:
Formula: Maximum of function, Quadratic equations common roots
$f^{\prime}(x)=x^{2}+2 b+a x$
$g^{\prime}(x)=x^{2}+a+2 b x$
$(2 b-a)-x(2 b-a)=0$
$\therefore x=1$ is the common root
Put $x=1$ in $f^{\prime}(x)=0$ or $g^{\prime}(x)=0$
$1+2 b+a=0$
$7+2 b+a=6$
