本题目来源于试卷: Integral Calculus，类别为 IB数学
[问答题]
Consider the function xf9*o 6g mu kr5fkiw3 htk+e)1fancf ,d --4y ocsd2;) 0zljy r*l(uqxyv q7+c $f(x)=\frac{\sqrt{x}}{2 \cos x}$, $\frac{\pi}{2}\lt x\lt \frac{3 \pi}{2}$ .
1. 1. Show that the x -coordinate of the maximum point on the curve y=f(x) satisfies the equation $1+2 x \tan x=0$ .
2. Determine the values of x for which f(x) is an increasing function.
2. Sketch the graph of y=f(x) , showing clearly the maximum point and any asymptotic behaviour.
3. Find the coordinates of the point on the curve y=f(x) where the normal to the curve is perpendicular to the line y=x . Give your answers correct to two decimal places.
Consider the region bounded by the curve y=f(x) , the x -axis and the lines
$x=\frac{3 \pi}{4}, x=\frac{4 \pi}{3} \text {. }$
4. The region is now rotated through $ 2 \pi $ radians about the x -axis. Find the volume of revolution, giving your answer correct to two decimal places.
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