A car starts from a point P at time t = 0 seconds and stops at point Q. The distance x, in metres, covered by it, in t seconds is given by x = t2(2 – t/3). Find the time taken by it to reach Q and also find distance between P and Q.

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TextDerivative as Rate of Change

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Overspeeding increases fuel consumption and decreases fuel economy as a result of tyre rolling friction and air resistance. While vehicles reach optimal fuel economy at different speeds, fuel mileage usually decreases rapidly at speeds above 80 km/h. The relation between fuel consumption F (l/100 km) and speed V (km/h) under some constraints is given as F = V²/500 – V/4 + 14. On the basis of the above information, answer the following questions :

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The volume of a cube is increasing at the rate of 6 cm³/s. How fast is the surface area of cube increasing, when the length of an edge is 8 cm?

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