By sketching the graphs of $y=3{{\mathrm{e}}^{x}}$ and $y=x+3$ or otherwise, solve the inequalit

Question

By sketching the graphs of $y=3{{\mathrm{e}}^{x}}$ and $y=x+3$ or otherwise, solve the inequality $3{{\mathrm{e}}^{x}}>x+3$.[3] Hence find $\displaystyle\displaystyle \displaystyle\int_{-2}^{2}{\left| 3{{\mathrm{e}}^{x}}-x-3 \right|\mathrm{d}x}$ , giving your answer in an exact form.[4]

Accepted Answer

${x 0}\;;\; {3\mathrm{e}^{-2} + 3\mathrm{e}^2 - 10}$

2010 JJC P1 Q10

2010 JJC P1 Q10

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