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The number of points in (-oo,oo), for wh...

The number of points in `(-oo,oo),` for which `x^2-xsinx-cosx=0,` is 6 (b) 4 (c) 2 (d) 0

A

6

B

4

C

2

D

0

Text Solution

Verified by Experts

The correct Answer is:
C
Here , `x^(2)= x sin x +cos x`

Let `f(x)=x^(2) and g(x)= x sin x+cos x `
We know that, the graph for `f(x)=x^(2)`
To plot, `g(x)= x sin x+cos x`
`g'(x) = x cos x + sin x-sinx`
`g'(x)= cos x" " ...(i)`
`g'' (x)=-x sin x+ cosx " "..(ii)`
Put `g'(x)0 rarr x cos x=0`
`:. x=0, (pi)/(2),(3pi)/(2),(5pi)/(2),(7pi)/(2)`

At `x=0,(3pi)/(2),(7pi)/(2),...., f''(x)gt0` , so minimum
At `x=(pi)/(2),(5pi)/(2),(9pi)/(2),...,f'(x) lt0`, so maximum
So, graph of f(x) adn g(x) are shown as

So, number of solution are 2.
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