Applications of Differentiation
Applications of Differentiation
The diagram shows a rectangle \(ABCD\) inscribed in a semi-circle with fixed radius \(r\) cm.
If \(AD = x\) cm, find an expression for the perimeter \(P\) and area \(S\) of rectangle \(ABCD\), in terms of \(r\) and \(x\).
Show that when \(S\) is a maximum, the value of \(P\) is \(3\sqrt{2}r\).
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Answer:\(P=2x+2\sqrt{r^2-\frac{x^2}{4}}\), \(S=x\sqrt{r^2-\frac{x^2}{4}}\), and at maximum area \(P=3\sqrt{2}r\)
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