[填空题]
The equation of a cuc15u 81a p(ydgzec(3bed f d*vat 3(i 2vczsu+pkg5 ;drve is y=-x$^2$ +8x -12.A section of the curve is shown on the diagram below, with the two x-intercepts labelled.
1.Find $\frac{dy}{dx}$.
$\frac{dy}{dx}$=-ax+b ; a= , b= .
2.Write down the coordinates of the local maximum.
the local maximum is located at (x, y) ; x= , y= .
3.Write down an integral representing the area of the shaded region.
its area is determined by A=$\int_{2}^{6}(-x^2+ax-b)dx$, a= , b= .
4.Find the area of the shaded region.
A=$\frac{a}{b}$, a= , b= .
