Functions

JEE Main 2015 Papers › Algebra questions › Functions

The graph of the function cosx.cos(x+2)-cos^2(x+1) is
1.A straight line passing through (0,-sin^2 1) with slope 2.
2.A straight line passing through (0,0)
3.A parabola with vertex(1,-sin^2 1)
4.A straight line passing through the point (pi/2,-sin^2 1) and parallel to the x-axis

#Mathematics #Algebra

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2 Answers

145

Ranadeep Roy ·2013-04-29 23:30:17

I think 4 Can be correct, though not sure of the correct approach.

for maxima, dy/dx=0

differentiating
-sinx.cos(x+2) -cosx.sin(x+2) +2.cos(x+2).sin(x+1)=0
=> sin2(x+1)=sin(x+2.cosx + cos(x+2)sinx
=> sin 2(x+1)=sin2(x+1)

so , it is becoming an identity. , which means that the function is at its maximum value at all points. So it has to be a straight line parallel to x axis
Moreover puttingx=pi/2 in f(x) we get -sin^21