Question

If the functions $f(x)=\frac{x^3}{3}+2 b x+\frac{a x^2}{2}$ 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:

• A. $\frac{3}{2}$
• B. 3
• C. 6
• D. 4

Answer 1

Answer: (C)

6

Answer 2

f′(x)=x2+2b+ax
g′(x)=x2+a+2bx
(2b−a)−x(2b−a)=0
∴x=1 is the common root
Put x=1 in f′(x)=0 or g′(x)=0
1+2b+a=0
7+2b+a=6
So, the correct option is (C) : 6