let f(x) = xk , k belongs to R.
the value of K so that f is differentiable (n-1) times at x=0, but not differentiable n-times at x=0 is:
a) n
b) n-1
c) (3n-2)/3
d) n.o.t.
tukka mari thi.. lag gaya tha.. par sahi method se koi try karo...
62if it is a polynomial it wont work
so it cant be a polynomial..
derivative of a polynomail remains a polynomial. (at the end it becomes zero!!)
So we have to think in terms of at best fractional terms
here the power will decrease by 1 on each differentiation..
so on n-1 derivatives, it will become...
x1/3 which will be zero at x=0 but its derivative will have -ve power of x! so it will not be defined!
62hence the answer is c) (3n-2)/3
think of a simpler example..
y= square root (x)
62@skygirl
a simpler question:
is √x differentiable at x=0??
what is its derivative?
1@bhaiya,
shouldn it be n-2 ??
like u c,
for f(x) = x1 , f'(x) = 1 , f"(x) =0 ... further we get same value.
so its diff for upto 2nd derivative.
=> if k=n, its diff upto n+1 derivatives and not diff at n+2 th derivative
=> for not geting diferentiated at n, shouldn k be n-2 ??
