If 4x + 3 |y| = 5 y , then y as a function of x is :

(a)differentiable at x=0

(b)continous for all x belonging to R

(c) dy/dx = 1/2 for all x >0

(d) dy / dx= 2 for all x >o

Dear Sanchit Gupta,

4x + 3 |y| = 5 y

If y=0, then x= 0

If y>0, then y = 2x

If y<0, then y=x/2

It is clear that y is continuous at all points.

If y>0, then dy/dx = 2

If y<0, then dy/dx = ½

Hence y is not differentiable at 0.

hence correct option is (b)

if x>0, then we observe from

4x + 3 |y| = 5 y  that y>0, hence (d) can also be considered if there are more than correct option to this problem.

but if we have to select only one option, then it will be (b), which is more obvious.

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nagesh

Hi Sanchit

4x + 3 |y| = 5 y

case 1     y>=0

   then 4x +3y =5y

   or           y=2x

case 2       y<0

   then 4x-3y =5y

    or       y= x/2

if you will plot a graph then you will find a sharp corner at x=0 so it is not differentiable at x=0

but it is continous for alll x

so option B & D are correct