If the functions f(x)=x^33+2bx+ax^22 and g(x)=x^33+ax+bx^2,a 2b have a common extreme poin…

Question

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

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

have a common extreme point, then $a+2b+7$ 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