本题目来源于试卷: Integral Calculus，类别为 IB数学
[问答题]
Consider the functionr7ja 8;zr010xvypp3 a. qon dkxw3,6wh0hd7tp ( :h dz.s fm;pevfh-b $f(x)=\frac{a e^{-x}}{b-a e^{-x}}$ where $a\lt 0, b\lt 0$ .
1. Show that $f^{\prime}(x)=\frac{-a b e^{-x}}{\left(b-a e^{-x}\right)^{2}}$ .
2. Explain why $f^{\prime \prime}(x)$ is never zero.
3. Find the equation of:
a. the vertical asymptote of f ;
b. the horizontal asymptote of f .
4. Draw a sign diagram for $f^{\prime}(x)$ .
5. If a=3 and b=1 ,
a. sketch the graph of f labelling all asymptotes;
b. find the area of the region enclosed by f , the x and y axes and the line $x=\ln 2$ .
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