本题目来源于试卷: Differential Calculus，类别为 IB数学
[问答题]
Consider the functio)qcor+gxv n wmvk;f4x *m1/l 9n 8ts4+q+fu szk4u4omx b v+54y e4uqb f$f(x)=\frac{\sqrt{x}}{2 \cos x}, \frac{\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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