Question

Taxa de Variacao de F(x)=3 e F(x)=1/3x+2

Answer 1

Olá, Michael.

 

A taxa de variação de uma função é dada por:

 

$<var>\frac{f(x+h)-f(x)}h</var>$

 

Portanto:

 

$<var>\text{Taxa de varia\c{c}\~ao de }F(x)=3:\\\\ \frac{F(x+h)-F(h)}h=\frac{3-3}h=0</var>$

 

$<var>\text{Taxa de varia\c{c}\~ao de }F(x)=\frac{1}{3x}+2: \\\\ \frac{F(x+h)-F(x)}h=\frac{\frac{1}{3(x+h)}+2-\frac{1}{3x}-2}{h}=\frac{x-(x+h)}{3x(x+h)}}\cdot\frac1{h}=-\frac{h}{3xh(x+h)}=\\\\=-\frac{1}{3x(x+h)}</var>$