The number of points in (-oo, oo), for which x2-x sinx-cosx = 0, is(A)

1.	The number of points in (-oo, oo), for which x2-x sinx-cosx = 0, is(A) 6(B) 4[JEE (Adva(C) 2
Answer» Let , f(x) = x²-xsinx – cosx F’(x) = 2x – xcosx – sinx +sinx F’(x) = 2x – xcosx =(0,-1) F(0) = -1 So, if we see there exists only two points as the point (0,-1) makes a curve at two points Hence , it has two solutions The answer is two.

The number of points in (-oo, oo), for which x2-x sinx-cosx = 0, is(A) 6(B) 4[JEE (Adva(C) 2

Answer»

Let , f(x) = x²-xsinx – cosx

F’(x) = 2x – xcosx – sinx +sinx

F’(x) = 2x – xcosx

=(0,-1)

F(0) = -1

So, if we see there exists only two points as the point (0,-1) makes a curve at two points

Hence , it has two solutions

The answer is two.