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Question Number 11473 by tawa last updated on 26/Mar/17

$$\mathrm{Show}\mathrm{that}\mathrm{the}\mathrm{graph}\mathrm{of}\mathrm{y}={\mathrm{x}}^3+{2\mathrm{x}}^2+\mathrm{x}+1,\mathrm{between}\mathrm{x}=-1\mathrm{and}\mathrm{x}=2$$$$\mathrm{lies}\mathrm{entirely}\mathrm{above}\mathrm{the}\mathrm{x}-\mathrm{axis}$$

Commented by prakash jain last updated on 28/Mar/17

$$y=x^3+2x^2+x+1$$$$=x(x^2+2x+1)+1$$$$=x{(x+1)}^2+1$$$$y>0forx>0$$$$-1⩽x⩽0$$$$x{(x+1)}^2>-1$$$$x{(x+1)}^2+1>0$$$$$$

Answered by sm3l2996 last updated on 26/Mar/17

Commented by tawa last updated on 26/Mar/17

$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}.$$

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