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Home » Let’s test $ s = \sqrt2 $: - iBuildNew

Let’s test $ s = \sqrt2 $: - iBuildNew

📅 April 29, 2026 👤 scraface

Apr 29, 2026

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📌 \( f(1) = a(1) + b = a + b \)

📌 Differentiate: \( f'(u) = 2(u - 1)Q(u) + (u - 1)^2 Q'(u) + a \), so \( f'(1) = a \)

📌 Compute \( f(1) \):

📌 \[ f(1) = 1^5 - 3(1)^3 + 2(1) + 8 = 1 - 3 + 2 + 8 = 8 \]

📌 \[ a + b = 8 \quad ext{(1)} \]

📌 Compute \( f'(u) \):

📌 \[ f'(u) = 5u^4 - 9u^2 + 2 \]

📌 \[ f'(1) = 5(1)^4 - 9(1)^2 + 2 = 5 - 9 + 2 = -2 \]

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