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For a function f(x, y), we are given f(100,200) = 45.1, fx(100,200) = 0.5 and fy(100,200) = − 0.35.?
Estimate f(100, 198)
1 Answer
- 7 years ago
Recall that:
L(x,y) = f(a,b) + f_x(a,b)(x - a) + f_y(a,b)(y - b)
where (a,b) is a given point that belongs in the domain of f. Given that f(100,200) = 45.1, f_x(100,200) = 0.5 and f_y(100,200) = − 0.35, we have:
L(x,y) = 45.1 + 0.5(x - 100) - 0.35(y - 200)
So at the point (100, 198), we obtain:
L(100,198) = 45.1 + 0.5(100 - 100) - 0.35(198 - 200)
= 45.8
which is the approximation of f at the point (100,198).
I hope this helps!
