Hey there! We receieved your request
Stay Tuned as we are going to contact you within 1 Hour
One of our academic counsellors will contact you within 1 working day.
Click to Chat
1800-5470-145
+91 7353221155
Use Coupon: CART20 and get 20% off on all online Study Material
Complete Your Registration (Step 2 of 2 )
Sit and relax as our customer representative will contact you within 1 business day
OTP to be sent to Change
How do we find the set of points where a particular function is differentiable when we have to check for the entire domain of the function? How to choose the expected points of discontinuity?
Dear Eshita,
Please note that for a function to be differentiable at a point we need the following conditions:
1. It should be defined and be continuous at that point.2. It's left hand and right hand derivatives should exist and be equal
Now first the first part. Generally you shall be given a function as a composition of some functions that you know and this could be piecewise over the x-axis (say one composition for one part of x-axis and another for another part)
e.g. y = sin(ln(x)) for x<0 and cos(ln(x)) for x >= 0First thing you should check where the functions are not defined. like ln(x) is not defined for x<=0, 1/x is not defined for x=0. See where you get these situations in your functions. The operands to these functions should not be coming to those values. Next check for continuity of those functions. Again you would know where a function is not continuous like step function is not continuous at x=0. Once you have these check where those functions were not differentiable themselves. Generally there are hardly any simple functions which are discontinuous at points where they are countinous. From simple I mean function like trigonometric, trigonometric inverses, exponentials, polynomials etc.
So basically compositions would now give you trouble mostly for boundary points. If boundary points are well defined and there is continuity then calculate RHD (right hand derivate) and LHD and see if they are equal. Now you are done :)
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.Regards,Askiitians Experts,Gokul Joshi
Get your questions answered by the expert for free
You will get reply from our expert in sometime.
We will notify you when Our expert answers your question. To View your Question
Win Gift vouchers upto Rs 500/-
Register Yourself for a FREE Demo Class by Top IITians & Medical Experts Today !