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Most Important Selected Qs for JEE AdvancedMathematicsApplication of Derivatives

Paragraph: Consider an open cylindrical reservoir whose cross-sectional view is as shown in the figure. The thickness of the wall of cylinder is 1 cm as shown in the figure & the volume of the reservoir is 27 ~cm ^3 . Let x & h be the radius and the height of the cylinder and v(x)= (x+a)^2+ b x + c x^2 , where v(x) represents the volume of the material required to construct the cylinder expressed as a function of rad

Options

  1. Ax = h
  2. B2 x = h
  3. Cx =2 ~h
  4. Dnone of these

Correct answer

A. x = h

Step-by-step solution

aligned & v^ (x)= 2(x+1)- 54 x^2 - 54 x^3 & =2 x^4+x^3-27 x-27 x^3 =2 x^3(x+1)-27(x+1) x^3 & =2 (x+1)(x-3) (x^2+3 x+9 ) x^3 aligned at x=3 function has global minima at x =3, ~h =3 from equation (i)

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