[填空题]
The equation of a cua,d31jho4o yp rve is k1m* cq+ie/ d0tda blb(d5)uj y=-x$^3$ +4x$^2$ +x -4.A section of the curve is shown on the diagram below, with the three x-intercepts labelled.
1.Find $\frac{dy}{dx}$.
$\frac{dy}{dx}$=-ax$^2$ +bx +c ; a= , b= ,c= .
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=$\int_{1}^{4}(-x^3+ax^2+x-b)dx$, a= , b= .
4.Find the area of the shaded region.
A=$\frac{a}{b}$, a= , b= .
