本题目来源于试卷: Differential Calculus，类别为 IB数学
[问答题]
Consider the function +1e*nnp00 p lofekyl- 0wenq( 1vg*x 0 jd;n0.g8o pplfjws-b$f(x)=-2 \sin ^{2} x+3 \sin 2 x+\tan x-3,0 \leq x<\frac{\pi}{2}$ .
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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