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This is the simplest factored form over the reals. - DNSFLEX

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 Use the Pythagorean identity: \( \sin^2(x) + \cos^2(x) = 1 \).

📌 So, \( \left(\frac{3}{5}\right)^2 + \cos^2(x) = 1 \) gives \( \frac{9}{25} + \cos^2(x) = 1 \).

📌 Solving for \( \cos^2(x) \) gives \( \cos^2(x) = 1 - \frac{9}{25} = \frac{16}{25} \).

📌 Since \( x \) is in the first quadrant, \( \cos(x) = \frac{4}{5} \).

📌 #### \(\frac{4}{5}\)

📌 The function \( f(x) = x^3 - 3x^2 + 4 \) has a local minimum at \( x = a \). Find the value of \( a \).

📌 First, find the derivative: \( f'(x) = 3x^2 - 6x \).

📌 Set \( f'(x) = 0 \) to find critical points: \( 3x(x - 2) = 0 \).

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