[填空题]
The equation of a curfkxxq4dv/ 4a5 gft gx3og/8 sr*7 i+lfp.w5x govdltzo 0-dme27-l )ive is y=-$x^{3}+4 x^{2}+x-4$ . A section of the curve is shown on the diagram below, with the three x -intercepts labelled.
1. Find $\frac{\mathrm{d} y}{\mathrm{~d} x}$ = - ax$^2$+ bx+c ; a= ,b= ,c= .
2. Write down the coordinates of the local maximum.
3. Write down an integral representing the area of the shaded region.
A=$\int_{1}^{4}\left(-x^{3}+a x^{2}+x-b\right) \mathrm{d} x$;a= ,b= .
4. Find the area of the shaded region.
A=$\frac{a}{b}$;a= ,b= .
