The number of points in the rectangle x- y - - 12 - x - 12 and -3 - y - 3 which lie on the curve y - x - sin x and at which the tangent to the curve is parallel to the x - axis is

Y = x + sin x nbsp; If dydx = 1 + cos x = 0, nbsp;then cos x = 1 or x = ±π, ± 3π ... nbsp; Also, y = ±π, ± 3π ... But for the given constraint on x and y ...

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Standard XI

Mathematics

Tangent of a Curve y =f(x)

The number of...

Question

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

0

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Solution

The correct option is A $0$
$y = x + sin x$
If $\frac{d y}{d x} = 1 + cos x = 0,$ then
$cos x = 1 or x = \pm π, \pm 3 π . . .$
Also, $y = \pm π, \pm 3 π . . .$
But for the given constraint on $x$ and $y$ , no such $y$ exists.
Hence, no such tangent exists.

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

The correct option is A 0y=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.

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

The correct option is A $0$
$y = x + sin x$
If $\frac{d y}{d x} = 1 + cos x = 0,$ then
$cos x = 1 or x = \pm π, \pm 3 π . . .$
Also, $y = \pm π, \pm 3 π . . .$
But for the given constraint on $x$ and $y$ , no such $y$ exists.
Hence, no such tangent exists.