JEE Mains · Maths · STD 12 - 5. continuity and differentiation
Let the function \(f(x)=\left(x^2+1\right)\left|x^2-a x+2\right|+\cos |x|\) be not differentiable at the two points \(x=\alpha=2\) and \(x=\beta\). Then the distance of the point \((\alpha, \beta)\) from the line \(12 x+5 y+10=0\) is equal to :
- A 5
- B 4
- C 3
- D 2
Answer & Solution
Correct Answer
(C) 3
Step-by-step Solution
Detailed explanation
\(f(x)=\left(x^2+1\right)\left|x^2-a x+2\right|+\cos |x|\) Notice that \(\cos (-x)=\cos x=\cos |x|\) which means \(\cos |x|\) is differentiable everywhere in \(x \in R\) \(\Rightarrow f(x)\) can be non differentiable where \(\left|x^2-a x+2\right|\) \(=0\)…
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