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

Step-by-step solution

f(x)= (x^2+1 ) |x^2-a x+2 |+ |x| Notice that (-x)= x= |x| which means |x| is differentiable everywhere in x R aligned & f(x) can be non differentiable where |x^2-a x+2 | & =0 aligned x^2-a x+2=0 4-2 a+2=0 a=3 (x^2-3 x+2 )=0 x=1,2 =1 distance of ( , ) from line aligned & 12 x+5 y+10=0 & |2(12)+5(1)+10| 13 = 39 13 =3 aligned