let-f-x-y-z-x-2-y-2-z-2-with-R-1-calculate-f-2-find-in-order-to-have-f-0-

Question Number 34912 by abdo imad last updated on 12/May/18

l e t f (x, y, z) = {(x^{2} + y^{2} + z^{2})}^{α} w i t h α \in R

1) c a l c u l a t e Δ f

2) f i n d α i n o r d e r t o h a v e Δ f = 0

Answered by tanmay.chaudhury50@gmail.com last updated on 13/May/18

△ f = d f (x, y . z)

= {(\frac{\partial \int}{\partial x})}_{y, z} d x + {(\frac{\partial f}{\partial y})}_{x, z} d y + {(\frac{\partial f}{\partial z})}_{x, y} d z

= α . {(x^{2} + y^{2} + z^{2})}^{α - 1} . 2 x . d x +

α . {(x^{2} + y^{2} + z^{2})}^{α - 1} . 2 y + α . {(x^{2} + y^{2} + z^{2})}^{α - 1} 2 z