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Calculus Solutions 26

# Calculus Solutions 26 - Answers to Odd-Numbered...

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Answers to Odd-Numbered Problems 23 %=0whentant=&;fm,=2at (i,\$),fmin=-2at (-+,-'\$) 1 25 (ax + by),, = W; (x2 + y2)min = 2 7 0 < c < f 29 The vectors head-to-tail form a [email protected] triangle. The outer angle is 120' 31 2 + &; 1 + fi; 1 + 35 Steiner point where the arcs meet 39 Best point for p = oo is equidistant from corners 41 grad f = (& ?+ y+ y,\/Z ?+ + 7); angles are 90-135-135 43 Third derivatives all 6; f = 5x3 + *x2 + \$29 + 5 y3 1 2 3 3 45 (&)n(s)m ln(1- ~ y ) ] ~ , ~ = n!(n - I)! for rn = n > 0, other derivatives zero; f = -xy - 2 - 3 - . . 47 All derivatives are e2 at (1,l); f N e2[l + (x - 1) + (y - 1) + i ( x - 1)2 + (x - l)(y - 1) + ?(y - I ) ~ ] 4 9 x = l , y = - 1 : f,= 2, f, = -2, f,, = 2, fx, = 0, f, = 2; series must recover x2 + y2 51 Line x - 2y = constant; x + y = constant 5 3 ~ f . , + z y f x , + f f , , ] ~ , ~ ; f x , > O a n d f x z f u v > f ~ a t ( ~ , ~ ) ; f x = f v = O 5 5 A x = - l , A y = - 1 57 f = x2(12 - 42) has fmax = 16 at (2,4); line has slope -4, y = 5 has slope = -4 59 If the fence were not perpendicular, a point to the left or right would be closer Section 13.7 Constraints and Lagrange Multipliers (page 519) 2k kkl 3 A = -4, Xmin = 2, Ymin = 2 1 f = x2+ (k- 2 ~ ) ~ ;
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