very difficult

1. "very difficult" piece function question

Hey, how would i do a question like this: Find the equation of the line that is tangent to the curve f(x) at two points. f(x)=(x+3)^2\quad for\;x<0 \qquad -x^2+8x-4\quad for\;x\ge 0 Thanks
2. "very difficult" limits question

\displaystyle\lim_{x\to\infty}\sqrt[3]{(x^3+5x^2)}-x