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Question

The point on the curve y=12x−x2, where the slope of the tangent is zero will be

A
(0,0)
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B
(2,16)
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C
(3,9)
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D
(6,36)
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Solution

The correct option is D (6,36)
Let the point be P(x,y)
y=12xx2
dydx=122x
(dydx)(x1,y1)=122x1

since slope of tangent is zero
so (dydx)x1,y1=0
122x1=0
2x1=12
x1=6

Also curve passing through tangent
y1=12x1x21
y1=12×636
y1=7236
y1=36
The points are (6,36).

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