$\text { Given } f ( x , y ) = 16 - x ^ { 2 } - y ^ { 2 } \text {, calculate } \Delta z \text { by evaluating } f ( 6,5 ) \text { and } f ( 6.4,5.29 ) \text {. }$ Round your answer to four decimal places.
A)-7.9441
B)-45.9441
C)-19.9441
D)0.1118
E)-4.8882

Question

Quizplus · Accepted Answer

To calculate $\Delta z$, we evaluate $f(6,5)$ and $f(6.4,5.29)$ and find the difference. First, $f(6,5) = 16 - 6^2 - 5^2 = 16 - 36 - 25 = -45$. Then, $f(6.4,5.29) = 16 - (6.4)^2 - (5.29)^2 = 16 - 40.96 - 27.9841 = -52.9441$. The change in $z$, $\Delta z$, is $f(6.4,5.29) - f(6,5) = -52.9441 - (-45) = -7.9441$.

Round Your Answer to Four Decimal Places