14 Application of Derivatives.pdf - Tutorial 14 Application of Derivative 1 The inside lane of a school running track consists of two straight sections

14 Application of Derivatives.pdf - Tutorial 14 Application...

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Tutorial 14: Application of Derivative 1 The inside lane of a school running track consists of two straight sections each of length x metres, and two semicircular sections each of radius r metres, as shown in the diagram. The straight sections are perpendicular to the diameters of the semicircular sections. The perimeter of the inside lane is 400 metres. (i) Show that the area, A m 2 , of the region enclosed by the inside lane is given by A = 400 r π r 2 . (ii) Given that x and r can vary, show that, when A has a stationary value, there are no straight sections in the track. Determine whether the stationary value is a maximum or a minimum. 2 In the diagram, S is the point (0, 12) and T is the point (16, 0). The point Q lies on ST , between S and T , and has coordinates ( x , y ). The points P and R lie on the x -axis and y -axis respectively and OPQR is a rectangle. (i) Show that the area, A , of the rectangle OPQR is given by 𝐴 = 12𝑥 − 3 4 𝑥 2 .
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  • Winter '19
  • Jeffrey Chiang

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