# The power produced by a dam is given by E = 16x^2 - 12x - 1000 MW where x is the height of the water. If the water level drops at 14 m/s what is the rate of change of power production. The power produced by a dam is given by E = 16x^2 - 12x - 1000 MW where x is the height of the water. The water level is dropping at a rate of 14 m/s. The rate of change of power due to this has to be determined. The...

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The power produced by a dam is given by E = 16x^2 - 12x - 1000 MW where x is the height of the water. The water level is dropping at a rate of 14 m/s. The rate of change of power due to this has to be determined. The rate of change of the water level `(dx)/(dt) = -14` .

The rate of change of the power production is given by `(dW)/(dt) = 32x*(dx/dt) - 12*(dx)/(dt)` . As the water level drops at 14 m/s, the power produced changes at a rate `32*x*(-14) - 12*(-14)`

=> -448x + 168 MW/s

The rate of change of the power production -448x + 168 MW/s