Question

Qual a taxa de variação máxima da função f(x,y,z)=ln(x. y². z³) no ponto (1,-2,-3)

Answer 1

$f(x,y,z)=\ln(xy^2z^3)=\ln x+2\ln y+3\ln z\\ \\ f_x=\dfrac{1}{x}\;,\; f_y=\dfrac{2}{y}\;,\;f_z=\dfrac{3}{z}\\ \\ \nabla f(1,-2,-3)= (1,-1,-1)\\ \\ \boxed{\text{Taza de variaci\'on m\'axima: }\|\nabla f(1,-2,-3)\|=\sqrt{3}}$