Math241 D1 Quiz#4 June 29, 2011
Name: Answer keys
1.[10pts] Find all the second partial derivatives fxx, fxy, fyx , fyy of the function
f(x, y) = x2
y.
Sol)
fx=2x
y, fy=โx2
y2(1)
fxx =2
y, fxy =โ2x
y2(2)
fyx =โ2x
y2, fyy =2x2
y3.(3)
2.[10pts] The function f(x, y) is differentiable at all points (x, y)โR2. Find the lin-
earization L(x, y) at the given point;
f(x, y) = x2y3,(1,2).
Sol)
fx= 2xy3, fy= 3x2y2(4)
L(x, y) = f(1,2) + fx(1,2)(xโ1) + fy(1,2)(yโ2) (5)
= 8 + 16(xโ1) + 12(yโ2) (6)
=โ32 + 16x+ 12y. (7)
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