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AP EAMCET201822 Apr 2018Evening ShiftMathematicsApplication of DerivativesActual

If the petrol burnt in driving a motor boat varies as the cube of the velocity, then the speed (in km / hour) of the boat going against a water flow of C kms / hour so that the quantity of petrol burnt is minimum is

Options

  1. A2 C 3
  2. B3 C 2
  3. C4 C 3
  4. D3 C 4

Correct answer

B. 3 C 2

Step-by-step solution

Let V>C the speed of motor boat, relative to water. In fact, relative to land, the motor boat moves with the speed V-C . The motor boat covers a distance S in S V-C ~h and consumption is f(v)=k v^3 S V-C , where k is a constant. The minimum of consumption is attained for aligned & f^ (v)=0 & k S (v-C) 3 v^2-v^3(1) (v-C)^2 =0 & 3 v^3-3 v^2 C-v^3=0 & 2 v^3-3 v^2 C=0 v= 3 C 2 . & aligned

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