Medium MCQ +4 / -1 PYQ · JEE Mains 2023

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 6 Correct answer
B $\frac{3}{2}$
C 3
D 4

Solution

$f'(x)=x^2+2b+ax$ $g'(x)=x^2+a+2bx$ $\Rightarrow x=1$ is common root $a+2b+1=0$

About this question

Subject: Mathematics · Chapter: Application of Derivatives · Topic: Tangents and Normals

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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 :

Solution

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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 :