JEE MAIN - Mathematics (2023 - 30th January Evening Shift - No. 8)
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 :
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 :
6
$\frac{3}{2}$
3
4
Explanation
$$f'(x)=x^2+2b+ax$$
$$g'(x)=x^2+a+2bx$$
$$\Rightarrow x=1$$ is common root
$$a+2b+1=0$$
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