A particle follows a path given by y = 4x^2 + 3. The particle is moving horizontally at 15 m/s. What is the rate of change of height at x = 8

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justaguide eNotes educator| Certified Educator

The path followed by the particle is given by y = 4x^2 + 3. It is moving horizontally at at rate of 15 m/s. `(dx)/(dt) = 15` .

`(dy)/(dt) = 8x*(dx)/(dt)`

=> `(dy)/(dt) = 8x*15`

=> `(dy)/(dt) = 120x`

At x = 8, `(dy)/(dt) = 960` m/s

The rate of change in the height of the particle at x = 8 is 960 m/s