QJEEM23Ma55fd: JEE Main 2023 Mathematics - Class 12 JEEM23Ma55fd Solution: If the functions and have a common extreme point, then is equal …

Question

Verified Solution • 2025–26 Session moderate

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 :

Accepted Answer

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

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

$\Rightarrow x=1$ is common root

$a+2b+1=0$

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