Let the function f(x)=(x²+1)|x²-ax+2|+ cos |x| be not differentiable at the two points x=α=2 and x=β. Then the distance of the point (α, β) from the line 12x+5y+10=0 is equal to:

Limit, Continuity and Differentiability: JEE Main 2025 Mathematics question

JEE Main 2025 · January, Unspecified (session-level dataset) · Q135

JEE Main 2025January, Unspecified (session-level dataset)MathematicsMediumLimit, Continuity and Differentiability420× since 2002

Let the function

f(x)=\left(x^2+1\right)\left|x^2-ax+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

12x+5y+10=0

is equal to: