JEE Mains · Maths · STD 12 - 5. continuity and differentiation
If the functions \(f ( x )=\frac{ x ^3}{3}+2 bx +\frac{a x^2}{2}\) 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 \(4\)
- B \(\frac{3}{2}\)
- C \(3\)
- D \(6\)
Answer & Solution
Correct Answer
(D) \(6\)
Step-by-step Solution
Detailed explanation
\(f ^{\prime}( x )= x ^2+2 b + ax\) \(g ^{\prime}( x )= x ^2+ a +2 bx\) \((2 b - a )- x (2 b - a )=0\) \(\therefore x =1 \text { is the common root }\) \(\text { Put } x =1 \text { in } f ^{\prime}( x )=0 \text { or } g ^{\prime}( x )=0\) \(1+2 b + a =0\) \(7+2 b + a =6\)
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