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Question

The number of points in the rectangle {(x,y)|12x12 and 3y3} which lie on the curve y=x+sinx and at which the tangent to the curve is parallel to the x - axis is

A
0
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B
2
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C
4
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D
8
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Solution

The correct option is A 0
y=x+sinx
If dydx=1+cosx=0, then
cosx=1 or x=±π,±3π ...
Also, y=±π,±3π ...
But for the given constraint on x and y, no such y exists.
Hence, no such tangent exists.

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