本题目来源于试卷: Properties of Functions，类别为 IB数学
[问答题]
Let $ f(x)=x^{4}-x^{3}-5 x^{2}+3 x+2$ , for $x \in \mathbb{R}$ .
1. Solve the inequality f(x)<0 .
2. For the graph of y=f(x) , find the coordinates of the local maximum point. Round your answers to three significant figures.
The domain of f is now restricted to [a, b] where a,$ b \in \mathbb{R}$ .
3. 1. Write down the smallest value of a<0 and the largest value of b>0 for which f has an inverse. Give your answers correct to three significant figures.
2. For these values of a and b , sketch the graphs of y=f(x) and $ y=f^{-1}(x)$ on the same set of axes, showing clearly the coordinates of the end points of each curve.
3. Solve the equation $f^{-1}(x)=-1$ .
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