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
Equation
Roots
Algebra
But try the problem first...
Answer:4
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.
I.S.I. & C.M.I. Entrance Program
Taught by students and alumni of I.S.I. & C.M.I.
Answer is 2