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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

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

Grade:12

2 Answers

askIITiansexpert nagesh
16 Points
12 years ago

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.

 

Please feel free to post as many doubts on our discussion forum as you can. If you find any question

Difficult to understand - post it here and we will get you the answer and detailed solution very quickly. We

are all IITians and here to help you in your IIT JEE preparation. All the best Sanchit Gupta

 

Regards,

Askiitians Experts

nagesh

 

 

Badiuddin askIITians.ismu Expert
148 Points
12 years ago

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

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