If the functions f(x)=(x^3)/(3)+2 b x+(a x^2)/(2) and g(x)=(x^3)/(3)+a x+b x^2, a 2 b have…

Question

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

and $g(x)=\frac{x^3}{3}+a x+b x^2, a 
eq 2 b$

have a common extreme point, then $a+2 b+7$ is equal to :

Accepted Answer

$f'(x)=x^2+2b+ax$

$g'(x)=x^2+a+2bx$

$$\Rightarrow x=1$$ is common root

$a+2b+1=0$

Solutions · 1