MATH 285-3 SUPPLEMENTAL HOMEWORK PROBLEMS
4.2 Extrema 1 Find all critical points and determine whether they are local maxima, local minima, or neither, for the following functions: (i) f (x, y, z) = x 2 - 4y 2 + z 2 + 8yz + 8x y, and (ii) f (x, y, z
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5-in-
Q 1: (15 points) Find and classify all of the critical points of the function
Math 285 Midterm 2
f(w,y) = $21; - 6112 315"-
l: r Chg-6'2 6 999- 6%: 0 eX(3-3> =0
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Math 285 Midterm 1 H Page 3 of 9
Q 2:(a) (7 points) Find the equation of the tangent plane to surface given by ez_y + 9322 = 2
at the point (1,1,1). L) e 25 W21, 2 :0
a 2 2 l
vw -826 e7 W 4
@215 +2942. 3
(b) (7 points) Let 041:2 + y2 + (222 = 4 be an e
Math 285 Midterm 2
Q 4: (15 points) Let f(:z:,y) =
f(a:,y) on the domain
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$2 + y2. Find the absolute maximum and minimum values of
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@ (9935"
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