Find constantsa andb so that the minimum for the parabolaf(x)=x2+ax+b is at the point(4,9). [Hint: Begin by finding the critical point in terms ofa.]

a=

b=

Enter the critical points in increasing order.

(a)Use the derivative to find all critical points.

x1=

x2=

x3=

(b)Use a graph to classify each critical point as a local minimum, a local maximum, or neither.

x1=

is

a local minimum

a local maximum

neither.

x2=

is

a local minimum

a local maximum

neither.

x3=

is

a local minimum

a local maximum

neither.