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Home » Set the derivative equal to zero to find critical points: - Abbey Badges

Set the derivative equal to zero to find critical points: - Abbey Badges

📅 February 26, 2026 👤 scraface

Feb 26, 2026

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2a x^2 + 2a y^2 + 2b x + 2c = 2a x^2 + 2a y^2 + 2b x + 2b y + 4c.
Equating coefficients: $ 2c = 2b y + 4c $ for all $ y $, which implies...
oxed{f(x) = kx^2 ext{ for some constant } k}
Question: Let $ a $ and $ b $ be complex numbers such that $ |a| = |b|...
eq b $. Find the value of $ rac{a + b}{a - b} + rac{a - b}{a + b} $.
Solution: Let $ S = rac{a + b}{a - b} + rac{a - b}{a + b} $. Combine...
S = rac{(a + b)^2 + (a - b)^2}{(a - b)(a + b)} = rac{2a^2 + 2b^2}{a^...
Since $ |a| = |b| = 1 $, $ a \overline{a} = 1 $ and $ b \overline{b} =...
S + \overline{S} = rac{(a + b)^2 + (a - b)^2}{a^2 - b^2} = rac{2a^2...
But $ a

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