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advanced functions

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A generator produces electrical power, P, in watts, according to the function P(R)=(120R)/(0.4+R)^2,
where R is the resistance, in ohms. Determine the intervals on which the power is increasing.

  • advanced functions - ,

    I would take the first derivative, and make it >0 and solve for the intervals.

  • advanced functions - ,

    1. P&prime&prime(R)=0
    ->gives you the points at which the slope of P(R) changes from increasing to decreasing or vice versa.

    2. Plug in a number between the intervals back into P&prime&prime(R)
    -> for example if you found:
    R= -1 and R = 4

    plug in 0 or 1 or 2 or 3 into P&prime&prime if its positive then the slopes are increasing on the interval from (-1, 4)

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