Science:Math Exam Resources/Courses/MATH200/December 2012/Question 03 (c)/Solution 1

We just plug in the values $(x,y)=(-1.02,0.97)$ into the linear approximation found in part b) $f(x,y)\approx -1-\frac{3}{2}(y-1)$

$f(-1.02,0.97)\approx -1-\frac{3}{2}(0.97-1)=-0.955$

[As a quick check, recall that $f(-1,1)=-1$, so our answer should be close to this (assuming our approximation is good).]