explain.....from reflections...;)

IIT JEE 1999: The function {\color{blue}(x^2-1)|x^2-3x+2| +\cos(|x|) is not differentiable at..

Now see there are 3 points of contention, 1,2 and 0. Take 0 first .. it is to come from cos(|x|). Simply see the derivative of cos x at zero. It is sin 0=0 . Hence at zero it is differentiable!

Now look at {\color{red}(x^2-1)(x-1)(x-2) its derivative at x=1 is zero! so the original function is differentiable at x=1!! Also derivative is not zero at x=2. Hence the original function is not differentiable at x=2! Verify it yourself!

Why this happens if very logical. dont think that there is any rocket science applicable here!

i am sure there is no rocket science used over here....but i think dat it is using some alien sciences...rocket sciences are easier...[3][3][3]

explain...neone....plzzzzzzzzzzzz...[2][2][2]

see the fact here is the if we have a |f(x)| then just after the point where f(x) is zero, the slope will be reflected on both sides... (if the f(x) is differentiable)

so this means that LHD=-RHD

but for differentiability, we want LHD=RHD

Using both the above, LHD=RHD=0

ok thank you bhaiya....

can u giva a sum on this???

simple ones would be what are the points where |x³-x| is differentiable

What are the points where |x⁴-2x²+1| is not differetiable