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Try this problem from I.S.I. B.Stat Entrance Objective Problem based on Number of points.

The number of points in the rectangle {(x,y)|\(-10 \leq x \leq 10 and -3 \leq y \leq 3\)} which lie on the curve \(y^{2}=x+sinx \) and at which the tangent to the curve in parallel to x axis, is

- 0
- 4
- 53361
- 5082

Equation

Roots

Algebra

But try the problem first...

Answer:4

Source

Suggested Reading

B.Stat Objective Problem 713

Challenges and Thrills of Pre-College Mathematics by University Press

First hint

here we see two graphs \(y^{2}=x+sinx\) and rectangle region

Second Hint

four such points here in which tangent is parallel to x axis

Final Step

or, number of required points=4.

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Answer is 2