Question

Which one is the graph of $q=\mathrm{xcos}\left(x\right)$?

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

$q\left(x\right)=\mathrm{xcos}\left(x\right)\mathrm{We}\mathrm{know}\mathrm{that}-1\le \mathrm{cosx}\le 1\Rightarrow -x\le \mathrm{xcos}\left(x\right)\le xi.e.,-x\le q\left(x\right)\le x...\left(1\right)i.e.,\mathrm{Graph}\mathrm{of}q\left(x\right)\mathrm{will}\mathrm{be}\mathrm{between}y=x\mathrm{and}y=-x.q\left(x\right)=0\Rightarrow x=0\mathrm{or}\cos \left(x\right)=0\mathrm{Now}\cos \left(x\right)=0\Rightarrow x=\left(n+1\right)\frac{\pi }{2},n\in Z\therefore q\left(x\right)\mathrm{is}\mathrm{zero}\mathrm{for}x=0,\left(n+1\right)\frac{\pi }{2}...\left(2\right)\mathrm{From}\left(1\right)\mathrm{and}\left(2\right),\mathrm{we}\mathrm{can}\mathrm{conclude}\mathrm{that}\mathrm{the}\mathrm{graph}\mathrm{of}q\left(x\right)=\mathrm{xcos}\left(x\right)\mathrm{is}\mathrm{option}\left(a\right).$