[填空题]
The following diagram s 4paw y)e4g1w9zusvx1hows t.tn ws.61atn(;fiuc she graph of the function
f(x)=ax$^3$+bx$^2$+cx+d , for -2≤x≤2.
1.State whether the function is increasing or decreasing at x=−1,0 and 1.
x=-1: the function is
x=0: the function is
x=1: the function is
2.Write down the value of d.
d=- .
The values of a and b are such that f(x) = -x$^3$ + $\frac{x^2}{2}$+cx+d.
3.Point K(−1,−1) lies on the graph of y=f(x). Find the value of c.
c=$\frac{a}{b}$;a= ,b= .
4.Use your graphic display calculator to find the coordinates of the local maximum, M.
f(x)=-x$^3$+$\frac{x^2}{a}$+$\frac{b}{c}$x-d; a= ,b= ,c= ,d= .
5.Find f'(x).
f'(x)=-ax$^2$+x+$\frac{3}{2}$; a= .
6.1.Calculate f′(0)=$\frac{a}{b}$;a= ,b= .
6.2.Find the equation of the tangent to the graph at the point (0,−1).
6.3.Write down the gradient of the normal to the graph at x=0.
7.Use your graphic display calculator to find the x coordinates where f(x)=−x, for the given domain.
