On a particular day, the power used in a particular state (in thousands of megawatts) could be approximated by the function P(t) = -0.006416t³ +0.1895t² -0.7477t + 19.94, where t is the number of hours since midnight, for Ost≤ 24. Find any relative extrema for power usage, as well as when they occurred. Find the derivative of P(t). P'(t)=

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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On a particular day, the power used in a particular state (in thousands of megawatts) could be approximated by the function \( P(t) = -0.006416t^3 + 0.1895t^2 - 0.7477t + 19.94 \), where \( t \) is the number of hours since midnight, for \( 0 \leq t \leq 24 \). Find any relative extrema for power usage, as well as when they occurred.

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Find the derivative of \( P(t) \).

\( P'(t) = \) [Box for the answer]
Transcribed Image Text:On a particular day, the power used in a particular state (in thousands of megawatts) could be approximated by the function \( P(t) = -0.006416t^3 + 0.1895t^2 - 0.7477t + 19.94 \), where \( t \) is the number of hours since midnight, for \( 0 \leq t \leq 24 \). Find any relative extrema for power usage, as well as when they occurred. --- Find the derivative of \( P(t) \). \( P'(t) = \) [Box for the answer]
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