题目

Nowadays more and more people are talking about genetically modified foods ( GM foods). GM foods develop from genetically modified organisms (有机体), which have had specific changes introduced into their DNA by genetic engineering techniques. These techniques are much more precise where an organism is exposed to chemicals to create a non­specific but stable change. For many people, the high­tech production raises all kinds of environmental, ethical, health and safety problems. Particularly in countries with long farming traditions, the idea seems against nature. In fact, GM foods4．已知函数f（x）=ax3+bx2+cx的导函数为h（x），f（x）的图象在点（-2，f（-2））处的切线方程为3x-y+4=0，且h′（-$\frac{2}{3}$）=0．（1）求函数f（x）的解析式；（2）若直线y=x是函数g（x）=$\frac{2k{e}^{x}}{{x}^{2}+2x+2}$f（x）的图象的一条切线，求k的值．