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Home » \[ h'(x) = rac1x^2 + 1 \cdot 2x = rac2xx^2 + 1 \] - Appfinity Technologies

\[ h'(x) = rac1x^2 + 1 \cdot 2x = rac2xx^2 + 1 \] - Appfinity Technologies

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Question: A teacher uses a digital tool where student engagement score $ e $ depends on time $ t $ (in minutes) as $ e(t) = t^2 - 4t + 7 $. If a activity runs for 6 minutes, what is $ e(6) $?

📌 Solution: Substitute $ t = 6 $ into the function:

📌 e(6) = 6^2 - 4(6) + 7 = 36 - 24 + 7 = 19

📌 Thus, the engagement score after 6 minutes is 19.

📌 \boxed{19}Question: A meteorologist models the change in atmospheric pressure over a 24-hour period with the function $ P(t) = t^3 - 6t^2 + 9t + 10 $, where $ t $ represents time in hours after midnight. At what time(s) does the pressure reach a local minimum or maximum?

📌 Solution: To find the local extrema of the function $ P(t) = t^3 - 6t^2 + 9t + 10 $, we first compute its derivative:

📌 P'(t) = 3t^2 - 12t + 9.

📌 Set $ P'(t) = 0 $ to find critical points:

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