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Question

The coordinates of the point on the curve x3=y(xa)2,a>0 where the ordinate is minimum

A
(2a,8a)
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B
(2a,8a9)
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C
(3a,27a4)
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D
(3a,27a16)
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Solution

The correct option is C (3a,27a4)
The ordinates of any point on the curve is given by y=x3(xa)2
dydx=x2(x3a)(xa)3
Now, dydx=0x=0 or x=3a
d2ydx2x=0=0andd2ydx2x=3a=72a5(2a)6>0
Hence y is minimum at x = 3a and is equal to 27a4

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