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Home » But this suggests no critical point. However, for minimum, consider behavior. - Crankk.io

But this suggests no critical point. However, for minimum, consider behavior. - Crankk.io

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 The function \(g(t) = t^2 e^t\) is differentiated. What is \(g'(t)\)?

📌 Use the product rule: \((uv)' = u'v + uv'\). Let \(u = t^2\), \(v = e^t\).

📌 \(u' = 2t\), \(v' = e^t\).

📌 \(g'(t) = 2t \cdot e^t + t^2 \cdot e^t = e^t(2t + t^2)\).

📌 #### \(e^t(2t + t^2)\)

📌 A car travels 150 km in 2 hours, then another 200 km in 3 hours. What is the average speed for the entire trip?

📌 Total distance = 150 km + 200 km = 350 km.

📌 Total time = 2 hours + 3 hours = 5 hours.

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