本题目来源于试卷: Trigonometric Functions，类别为 IB数学
[问答题]
Consider the functio+s g y1w3xpn+jn fhl)j8r k,:qkj 3rvchphmq d 6z:9,y, $f(x)=-2 \sin ^{2} x+3 \sin 2 x+\tan x-3,0 \leq x<\frac{\pi}{2}$ .
1. 1. Determine an expression for $f^{\prime}(x)$ in terms of x .
2. Sketch the graph of $y=f^{\prime}(x)$ for $ 0 \leq x<\frac{\pi}{2}$ .
3. Find the x -coordinate(s) of the point(s) of inflexion of the graph of y=f(x) , labelling these clearly on the graph of $y=f^{\prime}(x)$ .
2. Let $u=\tan x$ .
1. Express sin x in terms of u .
2. Express sin 2 x in terms of u .
3. Show that f(x)=0 can be expressed as $u^{3}-5 u^{2}+7 u-3=0 $.
3. Solve the equation f(x)=0 , giving your answers in the form $\arctan p$ , where $ p \in \mathbb{Z}$ .
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