It's easy to see that ie. use this and the fact that and substitute in the definition: and see that this goes to zero as . ( denotes the interior product, I'm assuming you're using the usual norm in )
Can anyone help me with this question???
prove f(x)=||x||^2 is differentiable using the definition of differentiability
where x is a vector in R^n. and ||x|| is the length of the vecotr(Not allowed to use use components of x)
x=(x1,x2,...xn)
The definitoin is lim as h->0, [f(a+h)-f(a) -c*h]/h =0
where c is the gradient of f,the function is differentiable at point a
I have absolutely no idea where to start, it's not like you have two distinct vairables..x,y....and prove differentiable at a particular point, and I am not allowed to use the components of x.How do i prove it's differentiable everywhere...
Anyone give me some hints?
Thanks so much
It's easy to see that ie. use this and the fact that and substitute in the definition: and see that this goes to zero as . ( denotes the interior product, I'm assuming you're using the usual norm in )