Answer
$\Delta f \simeq - 0.1$
Work Step by Step
We are given:
$f\left( {2,3} \right) = 8$, ${\ \ }$ ${f_x}\left( {2,3} \right) = 5$, ${\ \ }$ ${f_y}\left( {2,3} \right) = 7$
$\Delta x = - 0.3$ ${\ \ }$ and ${\ \ }$ $\Delta y = 0.2$
Let $\left( {a,b} \right) = \left( {2,3} \right)$. Using equation (5) we have the linear approximation in terms of the change in $f$:
$\Delta f \approx {f_x}\left( {a,b} \right)\Delta x + {f_y}\left( {a,b} \right)\Delta y$
$\Delta f \simeq 5\cdot\left( { - 0.3} \right) + 7\cdot0.2$
$\Delta f \simeq - 0.1$
