[填空题]
Consider the function kr1wa 4qrk,ao7 7cx f:vxm73t u/ ey;l2loh+8f5xbq o$f(x)=-\frac{1}{3} x+\frac{a}{2 x^{2}}$ , where a is a constant and $x \neq 0 $.
1. Find $f^{\prime}(x)$ = -$\frac{1}{a_1}$-$\frac{a}{x^3}$;$a_1$= .
The function f(x) has a local maximum at x=3 .
2. Show that a=-9 .
3. Find the y -coordinate of the local maximum of the function.f(x)=-$\frac{1}{3}$x-$\frac{b}{2x^2}$;b= .
4. Sketch the graph of f(x) , for $-6 \leq x \leq 8$ and $ -6 \leq y \leq 2 $.
5. State the values of x for which f(x) is increasing, .
6 . Find the x -intercept of the graph of the function f(x) .
7. Calculate $f^{\prime}(1)$ =$\frac{a}{b}$;a= ,b= .
8. Find the equation of the normal to the graph of y=f(x) at x=1 .
