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

Numbers of points (B.Stat Objective Question)

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

Key Concepts

Equation

Roots

Algebra

But try the problem first…

Source

B.Stat Objective Problem 713

Challenges and Thrills of Pre-College Mathematics by University Press

Try with Hints

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.